Question

Suppose that the current price of an asset is $80. After six months, there are two possible scenarios: 5+-$100 and 5 = $50. The exercise price of the call option is $90 and its expiration date is six months from now. The annual risk-free rate is 2%.

A) What is the hedge ratio?

B)

C) Using the present cash flow of arbitrage strategy, compute the size of the call premium?

D)What would be the put option on this asset?

Answer 1

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- 05:41 = vol4x 2 ENG, 14-05-2020 11 ... o X AU343 X ✓ fx AN AO AQ AR AS AT AU 1 AP SO = AV AW A - AM 343| 344 80 90 X = 2% 345 2 POSSIBILITIES FOR ST = 100 AND 50, FOR CALL = 100 - 90 = 10 ANDO RANGE OF S = 50 AND THAT OF CALL = 10 ACROSS THE 2 STATES Α 346 347 348 349 HEDGE RATIO = 350 Cu-Cd / uso - dso (10-0)/(100-50) = 0.200 351 352 353 ST=50 risk less portfolio BUY 1 SHARES WRITE 5 CALL TOTAL ST=100 100 354 355 356 357 358 50 -50 50 50 PAYOFF = 50 359 360 C PRESENT VALUE = 50/1.02 = 49.02 361 362 363 364 365 366 207 PORTFOLIO COST: 1S - 5C = (80 X 1) - 50 THE VALUE OF THE PORTFOLIO = 49.02 SO 80 - 5C = 49.02 5C = 30.98 CE 6.20 options Sheet1 CH-23 BOND portfolio sd excel BARTMAN chiptech Đ

- А. vol4x 2 ENG, 05:42 = 14-05-2020 ... o X ✓ AU390 I AM 367 368 X AN fx AO AP AQ AR AS AT AU AV AW A D FOR PUT OPTIONS 369 370 2 POSSIBILITIES FOR ST = 100 AND 50, FOR PUT = 0 AND 90-50 = 40 RANGE OF S = 50 AND THAT OF PUT = 40 ACROSS THE 2 STATES 371 372 373 HEDGE RATIO = 374 Pu- Pd / uso - DSO (0-40)/(100-50) = -0.800 375 376 377 378 379 380 381 risk less portfolio BUY 1 SHARES BUY 1.25 PUTS TOTAL ST=100 100 ST=50 50 50 100 [1.25 X 40] 100 382 PAYOFF = 100 PRESENT VALUE = 100/1.02 = 98.04 383 384 385 386 387 388 389 PORTFOLIO COST: 15 + 1.25P = (80 X 1) + 1.25P THE VALUE OF THE PORTFOLIO = 98.04 SO 80 + 1.25P = 98.04 1.25P = 18.04 P = 14.43 390 ܚܩܟ options Sheet1 CH-23 BOND portfolio sd excel BARTMAN chiptech | Đ