dstefan
06-14-2008, 04:34 PM
Chapter 3, Problem 17
You are long 1000 call options with strike 90 and three months to maturity. Assume that the underlying asset has a lognormal distribution with drift \mu = 0.08 and volatility \sigma = 0.2, and that the spot price of the asset is 92. The risk-free rate is r = 0.5$. What Delta-hedging position do you need to take?
Solution:
A long call position is Delta-hedged by a short position in the underlying asset. Delta-hedging the long position in 1000 calls is done by shorting 1000 \Delta(C) ~=~ 1000 e^{-q T} N(d_1) ~=~ 653.50 shares
You are long 1000 call options with strike 90 and three months to maturity. Assume that the underlying asset has a lognormal distribution with drift \mu = 0.08 and volatility \sigma = 0.2, and that the spot price of the asset is 92. The risk-free rate is r = 0.5$. What Delta-hedging position do you need to take?
Solution:
A long call position is Delta-hedged by a short position in the underlying asset. Delta-hedging the long position in 1000 calls is done by shorting 1000 \Delta(C) ~=~ 1000 e^{-q T} N(d_1) ~=~ 653.50 shares