Lecture 03 : Uncertainty in Financial Markets : Idea of Hedging — Transcript

Full transcript

1. 0:01[Music]
2. 0:22[Music]
3. 0:27welcome to the third lecture of
4. 0:30artificial intelligence for
5. 0:32economics in this segment that is in the
6. 0:34next couple of lectures we'll deal with
7. 0:37uncertainty in financial markets or
8. 0:39modeling
9. 0:40uncertainty now in artificial
10. 0:43intelligence uh a a key idea is to train
11. 0:48an agent to behave optimally in
12. 0:51environment where the outcomes are
13. 0:55uncertain and in economics
14. 0:58uncertainty uh is is in integral
15. 1:01part so in the next couple of lectures
16. 1:03we'll deal with uncertainty in financial
17. 1:06Market markets
18. 1:08especially the idea of
19. 1:10hedging and
20. 1:13risk great so let's get
21. 1:17started let's start with a very simple
22. 1:20example of cricket
23. 1:22betting the T20 World Cup is coming up
24. 1:25so uh you can you all of you must be
25. 1:28excited about cricket
26. 1:30so let's consider a following scenario
27. 1:32let's say an India versus Australia
28. 1:34cricket match is
29. 1:36happening okay and there are two
30. 1:38counters you have entered a room and
31. 1:40there are two
32. 1:41counters in counter one verat bets on
33. 1:47India and offers the following bet 25 is
34. 1:50to 1 what does this
35. 1:52mean what does this mean it simply means
36. 1:55that if uh I bet rupe 1 with V and verat
37. 2:01is betting on India so it means that
38. 2:04verat is hoping that India is going to
39. 2:06win so if I bet rupe 1 with verat and
40. 2:10Australia
41. 2:12wins okay so I'm betting rupe 1 with
42. 2:15verat that Australia will win and
43. 2:17Australia indeed
44. 2:19wins then verat will pay me 25
45. 2:23rupees and if India wins I will pay
46. 2:26verat one
47. 2:27rupee so this is the
48. 2:30uh bet a contract we can get into that's
49. 2:34what he's
50. 2:36offering in the other counter there is
51. 2:39Steve Steve on the other hand bets on
52. 2:41Australia so Steve Steve bets that
53. 2:44Australia is going to win win and he
54. 2:46offers offers a bet of 6 is to5 so what
55. 2:50does that mean it means that if I bet
56. 2:52rupee 1 with
57. 2:55Steve that India will win and India
58. 2:57indeed wins then Steve will pay me 6X
59. 3:02five rupees and if Australia wins I will
60. 3:05pay Steve one
61. 3:07rupee okay so this is the
62. 3:10scenario I have 100 rupees in my wallet
63. 3:13and I've entered the
64. 3:16room so what should I do should I bet
65. 3:20with
66. 3:21verat should I bet against verat or
67. 3:25should I bet against
68. 3:26Steve which counter should I go to and
69. 3:29place my bet
70. 3:31okay let's see so if I bet all my money
71. 3:34on verat against
72. 3:36verat okay that is I bet all my money on
73. 3:39Australia
74. 3:41winning then what is my
75. 3:43payoff if Australia indeed wins then
76. 3:46verat will pay me 2500
77. 3:49rupees but if India wins then I'll have
78. 3:53to pay verat 100
79. 3:56rupees right so my payoff isus 100 if
80. 3:59India
81. 4:01on the other hand if I bet all my money
82. 4:04on India that is I bet against
83. 4:07Steve then what's going to be my payoff
84. 4:10if India wins that is if Steve loses the
85. 4:13BET then Steve will pay me 6x5 into 100
86. 4:17remember he was paying 6x5 rupees for
87. 4:19every rupee bet so if 100 rupees of bet
88. 4:23is placed on the table he's going to pay
89. 4:25me 6x5 into 100 that's
90. 4:27120 but if Australia
91. 4:30wins then I will have to pay Steve the
92. 4:35money which I was betting which is 100
93. 4:38rupees great so these are my two options
94. 4:40I can either go to Steve or I can go to
95. 4:43verat but there is an inherent
96. 4:45limitation with both these
97. 4:47options what is
98. 4:50that these are win all lose all
99. 4:54options in the worst possible outcome I
100. 4:57will lose all my money
101. 5:02right
102. 5:04now uh that's a little harsh I don't
103. 5:07want that I don't want to lose all my
104. 5:09money that's too much of a risk I don't
105. 5:12want that can I mitigate my risk can I
106. 5:16eliminate this risk that's the next uh
107. 5:20that's the question I would want to
108. 5:22address that can I eliminate this risk
109. 5:25that in the worst possible case I will
110. 5:26lose all my money
111. 5:29let's see if I can do
112. 5:32that let's consider this let's say I bet
113. 5:36an x amount of money against
114. 5:40verat and 100 - x amount of money
115. 5:43against
116. 5:45Steve okay great now let's see what's
117. 5:48going to
118. 5:49happen now I've bet X Rupees against
119. 5:52verat
120. 5:54right so if Australia wins when I'm
121. 5:58betting against verat what am I saying
122. 6:00I'm saying that if Australia wins you
123. 6:03will pay me
124. 6:0625x right so uh I put X on the table and
125. 6:11Australia wins verat pays me 25x so I
126. 6:14get back
127. 6:1726x and against uh minus of course uh
128. 6:21100 which uh I have put on the
129. 6:25table right because I'm losing the bet
130. 6:27against Steve
131. 6:30so if Australia wins I'm winning the bet
132. 6:33against verat only and I'm losing the
133. 6:36bet against
134. 6:38Steve so what is my net payoff my net
135. 6:41payoff is 26x which I have with me minus
136. 6:45the 100 rupees which I which I put on
137. 6:47both the tables put
138. 6:49together right similarly if India wins
139. 6:53what will be my
140. 6:55payoff if India wins I lose the bet
141. 6:58against ver
142. 7:00but I win the bet against
143. 7:03Steve but how much will Steve pay me for
144. 7:05this bet so Steve is going to pay me
145. 7:08Steve will pay me this much and this was
146. 7:11the original amount which I put on the
147. 7:13table so I will get all this for
148. 7:16myself and 100 was the money I
149. 7:21bet okay so this is my payoff so this is
150. 7:24my payoff net payoff if India wins this
151. 7:27is my net payoff if Australia
152. 7:30wins
153. 7:32okay
154. 7:34great now is it possible that I will
155. 7:38make positive
156. 7:40profits no matter who
157. 7:42wins is that a
158. 7:45possibility let's
159. 7:47see when is my profit if India wins this
160. 7:52is my profit of India wins 26x - 100
161. 7:56when is this
162. 7:57positive when X is greater than
163. 8:003.85 this
164. 8:04one when austr uh when India wins what
165. 8:07is my payoff this is my the first is my
166. 8:10payoff when Australia wins when India
167. 8:12wins this is my
168. 8:14payoff now when will this be positive
169. 8:17this is always positive if x is less
170. 8:19than
171. 8:2854.55% lies in this interval 3.85 to
172. 8:3154.55%
173. 8:51[Music]
174. 9:00I'm actually betting on
175. 9:04both and thereby I'm reducing my
176. 9:09risk okay and X is the amount I'm
177. 9:13betting with
178. 9:14verat so if that lies in this particular
179. 9:17interval we see that I I will make a
180. 9:20positive profit no matter which team
181. 9:23wins okay so now I have zero
182. 9:27risk in the previous
183. 9:30uh slide we saw that we had huge risk I
184. 9:33ran the risk of losing all my
185. 9:36money but now I see that I will not lose
186. 9:40even a single
187. 9:42penny Okay no matter which team wins so
188. 9:45I have completely eliminated my
189. 9:49risk very
190. 9:51good let's move
191. 9:54on so if you just graphically plot it
192. 9:58you can see the yellow line is the
193. 10:02payoff if Australia wins it's a it's
194. 10:06it's a it's a profit function is a
195. 10:07function of
196. 10:09X the X which I choose so remember what
197. 10:13is X x is the amount I'm betting against
198. 10:16verat 100 - x is the amount I'm betting
199. 10:18against Steve so the yellow line is the
200. 10:21profit function as a function of
201. 10:24X when Australia wins the blue line is
202. 10:29the profit as a function of x if India
203. 10:33wins
204. 10:35okay fantastic and we see that if uh X
205. 10:41lies between 3.85 and 54.55%
206. 11:01fine so my next question would be okay I
207. 11:05can choose an X between 3.85 and 54.55%
208. 11:30right that's the next question which we
209. 11:31would want to answer we have eliminated
210. 11:34our risk great now we want to figure out
211. 11:37given that we have eliminated the risk
212. 11:39what is the maximum we can earn maximum
213. 11:42risk-free gain which we can have that's
214. 11:45our next objective NE next natural
215. 11:48objective okay so let's see by the way
216. 11:51what is the minimum guaranteed profit if
217. 11:54we go back to the previous
218. 11:55slide look at the diagram so let's say x
219. 11:58is here let's let's say this is
220. 12:014.5 okay if Australia wins what is my
221. 12:05payoff my payoff is this
222. 12:07much and if India wins what is my payoff
223. 12:10my payoff is this
224. 12:11much right so what is the minimum payoff
225. 12:14which I'm going to get here it is this
226. 12:17this payoff if Australia
227. 12:22wins on the other hand if I'm here let's
228. 12:24say this is 49 or
229. 12:27whatever now the payoff if India wins is
230. 12:30this
231. 12:30much and if Australia wins the payoff is
232. 12:33this
233. 12:35much now what is the minimum guaranteed
234. 12:37payoff it's this much the payoff if
235. 12:41India wins here the minimum payoff is if
236. 12:43Australia wins here the payoff is if
237. 12:45India wins the minimum payoff the
238. 12:48minimum guaranteed
239. 12:49payoff and both are clearly
240. 12:54positive so the minimum guaranteed
241. 12:57profit function is this this this is my
242. 13:00payoff if India wins sorry this is my
243. 13:03payoff if Australia wins and this is my
244. 13:05payoff if India
245. 13:07wins right I hope you remember this from
246. 13:11the previous slides this is my payoff if
247. 13:13Australia wins this is my net payoff if
248. 13:15India wins net
249. 13:18profit right so this is if Australia
250. 13:22wins this is if India
251. 13:26wins and the minimum guaranteed payoff
252. 13:28is the thus minimum of these two because
253. 13:30I don't know who is going to
254. 13:32win
255. 13:34great and this is the minimum guaranteed
256. 13:37payoff which I want to
257. 13:39maximize so I'm the Gambler so what is
258. 13:41my optimization problem the gambler's
259. 13:44optimization
260. 13:45problem well it is to maximize this
261. 13:48minimum
262. 13:50payoff in the risk-free interval which
263. 13:53is X belonging to this
264. 13:55interval right that's my optimization
265. 13:57problem now
266. 14:00correct great now if we solve this
267. 14:03optimization problem we will see that
268. 14:07this function this function which we
269. 14:10have is
270. 14:12maximized when the when the two
271. 14:14arguments of the Min are
272. 14:17equal
273. 14:19okay and it turns out that it's
274. 14:21maximized when X star is
275. 14:277.80 okay that's the minimum gu if I
276. 14:31that's the choice of X which will lead
277. 14:33to the minimum guaranteed
278. 14:37profit
279. 14:38okay fine by the way if I choose xar
280. 14:42equal to
281. 14:457.8 what will be that risk-free
282. 14:48profit well it'll simply be something
283. 14:51like this if we calculate it'll simply
284. 14:53be 26 into
285. 14:567.80 - 100 and if we calculate it turns
286. 15:00out to
287. 15:03102
288. 15:06okay and that's the minimum guaranteed
289. 15:09profit which I can
290. 15:12earn how much money did I have initially
291. 15:15in my wallet 100 rupees and I see that
292. 15:19if I enter enter the gambling room with
293. 15:21100
294. 15:22rupees and verat and Steve are offering
295. 15:25the bets which they are
296. 15:26offering then I can end up with 102
297. 15:31rupees of guaranteed
298. 15:33profit okay which is more than
299. 15:37100% fantastic that is wonderful right
300. 15:40and it's
301. 15:43guaranteed
302. 15:46okay so that's what we
303. 15:49see xar is 7.8 and that gives me a 102
304. 15:55that's my
305. 15:57profit now
306. 16:01let's understand these
307. 16:03terms the idea which we saw here is the
308. 16:06idea of mitigating or eliminating Risk
309. 16:09by betting on both sides which I spoke
310. 16:10about a few minutes
311. 16:13earlier a strategy which generates
312. 16:16guaranteed returns is called an
313. 16:20arbitr
314. 16:22okay now what is arbitrage Arbitrage is
315. 16:27basically in a way find finding a
316. 16:30loophole by the way can you can you tell
317. 16:32me what's the loophole in the previous
318. 16:35example which we just worked out why
319. 16:37can't it exist in reality why can't two
320. 16:40people offering such a bet in a gambling
321. 16:42room it can't exist can you tell me why
322. 16:45try to guess the reason is think about
323. 16:48it let's say I have no money in my
324. 16:50wallet I just borrow 100 rupees from
325. 16:55somebody I go to the uh
326. 16:59I go to the uh gambling
327. 17:01room and I bet the way I
328. 17:04did and I will make a profit of
329. 17:08102 right so I will not only get my 100
330. 17:12rupees back the principal but I will
331. 17:14also earn guaranteed 102 rupees and the
332. 17:17100 rupees which I borrowed I can give
333. 17:19it
334. 17:20back which means I can make 102 rupees
335. 17:24out of nothing at any point of
336. 17:27time if that's the case I will keep on
337. 17:30making such 102 rupees every hour or
338. 17:34every minute which will make me a
339. 17:37trillionaire or or a or a multi-
340. 17:39trillionaire in 5 days but that can't
341. 17:43happen that will that will bring the
342. 17:45world crashing
343. 17:46down okay so such a scenario is called
344. 17:49an
345. 17:50Arbitrage example of financial Arbitrage
346. 17:53which we see in the financial markets is
347. 17:55bcn arbitrage often a particular stock
348. 17:58trade at different values in the Bombay
349. 18:01Stock Exchange and the National Stock
350. 18:02Exchange okay which should not happen if
351. 18:05it happens what's the problem the
352. 18:07problem is simple I will buy a unit from
353. 18:09the Bombay Stock
354. 18:11Exchange let's say at 10 Rupees and
355. 18:14let's say if it is trading at 12 rupees
356. 18:15in the National Stock Exchange I will
357. 18:17sell it in the National Stock
358. 18:19Exchange and uh I will make a profit of
359. 18:21two I buy from BSE sell in NSE or vice
360. 18:25versa and make profits and I keep making
361. 18:28profits
362. 18:29still all the money in the world belongs
363. 18:31to me okay which is
364. 18:36impossible great so we have talked about
365. 18:38hedging an
366. 18:41Arbitrage now a little
367. 18:43um extension of the example which we
368. 18:46just uh talked about we saw that if we
369. 18:50enter the gambling
370. 18:52room uh and verat and Steve are offering
371. 18:55the bets which they're
372. 18:56offering 25 is to 1 6X 5 is to
373. 19:011 uh I can make a guaranteed profit of
374. 19:05102 but then I'm not happy with
375. 19:08102 I'm a greedy man I want more money
376. 19:13okay and what if I decide to take a
377. 19:16little bit of risk and earn more profit
378. 19:19can I do
379. 19:21that the answer is of course yes if I
380. 19:25bet all my money against verat then
381. 19:29I can make 2500 if Australia
382. 19:32wins but I also have the risk of losing
383. 19:35all my
384. 19:36money okay so this is the risk and
385. 19:39return which I'm Tor
386. 19:40between which every investor in the
387. 19:43financial Market is torn
388. 19:44between
389. 19:46okay that here I can make a risk-free
390. 19:49return of 102 but on the other
391. 19:52hand uh I can make 2500 which is a which
392. 19:55is a hell lot more but I I'm also
393. 19:59susceptible to losing all my money okay
394. 20:03great I don't want that that is why I
395. 20:06wanted the risk free return but now I
396. 20:08say that okay fine risk-free 102 is very
397. 20:11good but let's say I can't afford to
398. 20:14lose all my money but I can take a risk
399. 20:16of 10
400. 20:18Rupees so I will simply take a little
401. 20:22risk okay such that I will lose 10
402. 20:25Rupees at
403. 20:27Max I will allow myself this small
404. 20:31window of Lo of losing 10 Rupees if in
405. 20:34the worst
406. 20:35case if that's the scenario what's the
407. 20:39maximum profit which I can
408. 20:42earn okay given that my maximum loss is
409. 20:4710
410. 20:50Rupees let's see let's try to let's try
411. 20:53to solve this now
412. 20:59if I if I choose xar at 7.8 my
413. 21:04guaranteed profit was
414. 21:06102 now let's say if I move a little bit
415. 21:09to the right and I
416. 21:13choose my X here somewhere here
417. 21:19maybe let's say this is my choice of x
418. 21:22to the right of
419. 21:2754.55% Zone The risk-free Zone and I'm
420. 21:31choosing an x to the right of
421. 21:5754.55% 4
422. 21:5936 so if I choose this
423. 22:02x which is out of the safe Zone this is
424. 22:04my safe Zone remember 3.85 to 54.55%
425. 22:29so huge profit and a little risk now
426. 22:32whether I would do it or not depends on
427. 22:35my psychological makeup okay so uh it's
428. 22:40a risk if I if I choose to if I choose
429. 22:43to eliminate my risk completely my
430. 22:46profit is
431. 22:48102 if I choose to take a little bit of
432. 22:50risk of 10 Rupees that's the max I can
433. 22:53lose then my profit shoots up to
434. 22:571436 so this is the risk return
435. 22:59trade-off the risk and profit tradeoff
436. 23:03which you see in financial markets and
437. 23:06in
438. 23:07life great a little term which I want to
439. 23:11introduce you which you will encounter
440. 23:13in all uh finance and in probability
441. 23:17textbooks it is fair bet and implied
442. 23:21probability okay now what is a fair
443. 23:25bet a bet as you saw is a Rand variable
444. 23:30right or or the winnings from a bet is a
445. 23:33random
446. 23:35variable a bet or winnings from a bet
447. 23:38it'll is called a fair is called
448. 23:41fair if expectation of that random
449. 23:44variable is
450. 23:46zero
451. 23:47okay now in our example let us assume
452. 23:50that uh Ste verat and Steve are both
453. 23:53offering Fair bets and they also think
454. 23:55they're offering Fair
455. 23:56bets okay
456. 23:59then what is virat's expected
457. 24:02payoff well Virat is also having some
458. 24:05probability in mind which he thinks
459. 24:07India will win when he's when he's
460. 24:09betting he must be having something in
461. 24:11mind some probability in mind right so
462. 24:14what is virat's expected payoff if India
463. 24:17wins he will get get a payoff of plus
464. 24:20one if India loses he'll he'll get a
465. 24:23payoff of minus- 25 that's the bet he's
466. 24:26offering right so minus1 into
467. 24:29probability of India winning according
468. 24:30to
469. 24:31verat plus -25 into probability of
470. 24:34Australia winning according to
471. 24:37verat okay this PV end this is the
472. 24:41probability of India willing winning
473. 24:43according to verat this is virat's
474. 24:45implied probability that India will
475. 24:49win
476. 24:51okay if we solve this we get that vat's
477. 24:54implied probability is 25 by 26 that
478. 24:57India will win
479. 24:59okay so assuming that verat believes in
480. 25:01offering a fair
481. 25:03bet then uh that's the implied
482. 25:06probability of India winning according
483. 25:08to
484. 25:09vat okay similarly we can compute the
485. 25:13implied probabilities uh which of India
486. 25:16winning and Australia winning according
487. 25:18to
488. 25:19Steve
489. 25:22great now we have got an idea of risk
490. 25:25and profit
491. 25:29so let's move on to financial
492. 25:36markets let's move on to financial
493. 25:38markets and see what instruments we have
494. 25:41got in order to uh mitigate
495. 25:46risk so first in today's lecture we'll
496. 25:49talk
497. 25:50about two uh key financial
498. 25:55instruments the call and the put and
499. 25:58we'll talk about other kinds of
500. 26:00instruments in the in the in the in the
501. 26:02subsequent
502. 26:05lectures first let's take an example
503. 26:07let's start with an
504. 26:09example consider the TCS stock
505. 26:12price let's say the TCS stock price
506. 26:15today is
507. 26:173416 now I want to buy a TCS stock right
508. 26:20now but I have a feeling I have a hunch
509. 26:24that the market will crash and the TCS
510. 26:26stock price will go down to
511. 26:293316 instead of 3416 it'll go down to
512. 26:323316 that is by 100
513. 26:35rup okay so I'm tempted to wait and buy
514. 26:39later byy tomorrow on the 10th of
515. 26:43September so it seems that waiting till
516. 26:4510th of September might be good but what
517. 26:48if the crash doesn't happen what if the
518. 26:51price goes up to
519. 26:533500 then I will
520. 26:56regret right then I will think that ah I
521. 26:59wish I had bought it for
522. 27:023416 right so I'm confused should I wait
523. 27:07till 10th of September or uh I should
524. 27:11buy it
525. 27:15now now if there is a option which
526. 27:19allows me to buy a TCS stock on 10th of
527. 27:23September at today's price which is
528. 27:263416 then my fear will be gone right
529. 27:31what is my fear that the price will R
530. 27:33rise to
531. 27:3435 but if somebody gives me the option
532. 27:37gives me the assurance that don't worry
533. 27:40you can buy uh the TCS stock at 3416 on
534. 27:4410th of
535. 27:45September then I'll be relieved of this
536. 27:47pressure and I will take the risk of
537. 27:51waiting if the price comes down to
538. 27:533316 fantastic if it goes to 35 even
539. 27:58then it doesn't matter I have a
540. 28:00insurance that I can buy it at
541. 28:033416 okay this insurance or right is
542. 28:08called a call
543. 28:10option
544. 28:12okay this right is called a call call
545. 28:15option where the expiration date is 10th
546. 28:17of September and the strike price is
547. 28:223416 now why should anybody let's say
548. 28:25why should TCS give me this right for
549. 28:26free or anybody should give me this
550. 28:29right for free no they
551. 28:31won't nobody would so I'll have to buy
552. 28:34this right so a call option is a right
553. 28:38to buy a particular asset at a
554. 28:41particular price at some point in the
555. 28:44future okay okay somebody who buys a
556. 28:48call option that is somebody who buys
557. 28:51this right is said to go long on a call
558. 28:54option these are just terms
559. 28:56used and some somebody who sells this
560. 28:59right to some other
561. 29:00person so if I give you the right to buy
562. 29:05TCS stock at 3416 from
563. 29:10me on 10th of September then I'm selling
564. 29:13the call option then it is said that I
565. 29:16go short on a call
566. 29:19option okay
567. 29:22great so more formally this is what it
568. 29:25is a call option is a contract which
569. 29:27gives the owner the right to buy an
570. 29:29asset at an agreed upon price okay it is
571. 29:33denoted by
572. 29:35CEST e is the strike price that is the
573. 29:40price at which the call option allows
574. 29:43you to buy the asset at the expiration
575. 29:47date the expiration date is T that is
576. 29:50after T months or t days and S is your
577. 29:54underlying asset which is being bought
578. 29:55or sold in this case it was the TCS
579. 29:59stock
580. 30:01great so if uh let's say if I go long on
581. 30:06a call
582. 30:07option that is if I buy a call option
583. 30:11what is my
584. 30:13payoff well let's say uh I buy a call
585. 30:17option which allows me to uh buy one
586. 30:22unit
587. 30:23of an asset or one unit of a stock at e
588. 30:29Rupees at some point in the future at
589. 30:31the expiration
590. 30:33date now if the price becomes e+
591. 30:3810 if the price at the expiration date
592. 30:42this is the stock at the expiration date
593. 30:45if it becomes e+ 10 then what will
594. 30:48happen
595. 30:50well I have the right to buy the co buy
596. 30:54the stock at what price e so I will buy
597. 30:57the stock at Price e and sell it in the
598. 31:00Market at rupees e+ 10 so what will be
599. 31:03my payoff 10 Rupees I will make this
600. 31:06much this much of profit so as the stock
601. 31:09price at the expiration date goes up as
602. 31:12the price of the underlying asset at the
603. 31:14expiration date goes up my payoff will
604. 31:17go up who am I I'm the buyer or holder
605. 31:21of the call
606. 31:22option okay what if the price of the
607. 31:25asset or the stock price goes below
608. 31:29E well then I will not exercise the call
609. 31:32option at all because it will be silly
610. 31:34of me to do
611. 31:35so okay so let's say if at the
612. 31:38expiration date the price is e minus
613. 31:4110 that is the stock is available in the
614. 31:43market that particular asset is
615. 31:45available in the Market at Price e minus
616. 31:4910 now the call option is giving me a
617. 31:52right to buy that asset at
618. 31:54EES but why will I use that right I I
619. 31:58can anyway buy it in the Market at e
620. 31:59minus 10 Rupees at a cheaper price so
621. 32:02this right which I
622. 32:04have by the virtue of owning this call
623. 32:06option is
624. 32:08useless so my payoff is zero so it is
625. 32:12zero
626. 32:13here so this is how the payoff looks
627. 32:16like of course here I'm assuming that
628. 32:18the call option is call option does not
629. 32:20have any
630. 32:22price if we take the price into account
631. 32:25then the entire payoff
632. 32:29uh graph will shift down by an amount P
633. 32:33which is this pce that's the price of
634. 32:35the call
635. 32:37option okay
636. 32:40great so I will stop here we'll talk
637. 32:43about put options in the next lecture
638. 32:47and we'll look
639. 32:48at uh different kinds of financial
640. 32:51instruments which we can design with put
641. 32:53and
642. 32:54call but that'll happen in the next
643. 32:56lecture so I'll see you in the next
644. 32:58lecture thank you