(b) Consider two options on the same stock and same time to maturity but with different strike prices. For option A, the strike price (K1) is equal to 10 USD, while for option B, the strike price (K2) is equal to 9.5 USD. The current stock price (S) is equal to 10 USD. There are no dividends and the risk - free is 3% p.a. In calculating the arbitrage - free option prices an investor's volatility estimate is 15% p.a. Yet option A trades for 0.8 USD and option B for 1 USD. i. Compare the implied volatilities of both options A and B to the investor's estimate of 15% ii. ii. Identify the optimal strategy in the two options. Using the investor's volatility estimate, derive the delta - neutral position of your call option portfolio.
(b) Consider two options on the same stock and same time to maturity but with different strike prices. For option A, the strike price (K1) is equal to 10 USD, while for option B, the strike price (K2) is equal to 9.5 USD. The current stock price (S) is equal to 10 USD. There are no dividends and the risk - free is 3% p.a. In calculating the arbitrage - free option prices an investor's volatility estimate is 15% p.a. Yet option A trades for 0.8 USD and option B for 1 USD. i. Compare the implied volatilities of both options A and B to the investor's estimate of 15% ii. ii. Identify the optimal strategy in the two options. Using the investor's volatility estimate, derive the delta - neutral position of your call option portfolio.
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:(b) Consider two options on the same stock and same time to maturity but with
different strike prices. For option A, the strike price (K1) is equal to 10 USD, while
for option B, the strike price (K2) is equal to 9.5 USD. The current stock price (S)
is equal to 10 USD. There are no dividends and the risk - free is 3% p.a. In
calculating the arbitrage - free option prices an investor's volatility estimate is 15%
p.a. Yet option A trades for 0.8 USD and option B for 1 USD. i. Compare the
implied volatilities of both options A and B to the investor's estimate of 15% ii. ii.
Identify the optimal strategy in the two options. Using the investor's volatility
estimate, derive the delta - neutral position of your call option portfolio.
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