27. Bonus Question: A one-year European call option on XYZ with a strike price of $220 is trading at $6.58. The current stock price for Microsoft is $218. Suppose that the risk-free rate is 1%, whereas the dividend yield on Microsoft is 0. According to the Black-Scholes model (BSM), what is the implied annual volatility? Choose the best answer. (a) 0.075 (b) 0.167 (c) 0.114 (d) 0.305 28. Bonus Question Use risk-neutral valuation to value a derivative at time t that pays off $1 at time T if the price at maturity, ST goes below K, i.e., ST < K. Let St denote the price of a non-dividend paying stock at time t. Express the risk-neutral price of the derivative using the spot price (St), the strike price (K), the risk-free rate (r), the stock volatility (o), and time to maturity (7 = T - t). Hint: recall that under risk-neutral valuation and GBM, the stock price is given by Ste(r-)T+0√TXE where ~ N(0, 1) (a) Φ ( ) log()-(-)r αντ log()+(r-)r O√T (b) > ) (c) Φ (d) Þ log($)+(r−²²)r O√T log()-(r-)r O√T ST=
27. Bonus Question: A one-year European call option on XYZ with a strike price of $220 is trading at $6.58. The current stock price for Microsoft is $218. Suppose that the risk-free rate is 1%, whereas the dividend yield on Microsoft is 0. According to the Black-Scholes model (BSM), what is the implied annual volatility? Choose the best answer. (a) 0.075 (b) 0.167 (c) 0.114 (d) 0.305 28. Bonus Question Use risk-neutral valuation to value a derivative at time t that pays off $1 at time T if the price at maturity, ST goes below K, i.e., ST < K. Let St denote the price of a non-dividend paying stock at time t. Express the risk-neutral price of the derivative using the spot price (St), the strike price (K), the risk-free rate (r), the stock volatility (o), and time to maturity (7 = T - t). Hint: recall that under risk-neutral valuation and GBM, the stock price is given by Ste(r-)T+0√TXE where ~ N(0, 1) (a) Φ ( ) log()-(-)r αντ log()+(r-)r O√T (b) > ) (c) Φ (d) Þ log($)+(r−²²)r O√T log()-(r-)r O√T ST=
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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Transcribed Image Text:27. Bonus Question: A one-year European call option on XYZ with a strike price of $220 is trading
at $6.58. The current stock price for Microsoft is $218. Suppose that the risk-free rate is 1%,
whereas the dividend yield on Microsoft is 0. According to the Black-Scholes model (BSM), what
is the implied annual volatility? Choose the best answer.
(a) 0.075
(b) 0.167
(c) 0.114
(d) 0.305
28. Bonus Question Use risk-neutral valuation to value a derivative at time t that pays off $1 at time
T if the price at maturity, ST goes below K, i.e., ST < K. Let St denote the price of a non-dividend
paying stock at time t. Express the risk-neutral price of the derivative using the spot price (St), the
strike price (K), the risk-free rate (r), the stock volatility (o), and time to maturity (7 = T - t).
Hint: recall that under risk-neutral valuation and GBM, the stock price is given by
ST = Ste(r)T+0√TXE
where ~
(a) Φ
(b)
(c) Φ
N(0, 1)
log()+(r-)T
O√T
(d) Φ
log(5)-(r_²²2)r
αντ
log()+(r-2²)r
O√T
log($)-(r–²²)r
O√T
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