The Delta-Gamma Approximation: Practice Problems and Solutions
The Actuary's Free Study Guide for Exam 3F / Exam MFE - Section 47
This section of sample problems and solutions is a part of The Actuary's Free Study Guide for Exam 3F / Exam MFE, authored by Mr. Stolyarov.This is Section 47 of the Study Guide. See Section 1 here. See Section 2 here. See Section 3 here. See Section 4 here. See Section 5 here. See Section 6 here. See Section 7 here. See Section 8 here. See Section 9 here. See Section 10
A market-maker sells assets or contracts to buyers and buys them from sellers. He is an intermediary between the buyers and sellers. A market-maker's function is in contrast to proprietary trading, which is "trading to express an investment strategy" (McDonald, p. 414).
A delta-hedged position is a position designed to earn the risk-free rate of interest and is used to offset the risk of an option position.
The delta-gamma approximation is used to estimate option price movements if the underlying stock price changes.
The delta-gamma approximation for call options can be expressed via the following formula:
C(St+h) = C(St) + є∆(St) + (1/2)є2Γ(St)
For a put option, the same formula holds, but delta is now negative - so the put price will decrease if the stock price increases.
Meaning of variables:
St = stock price at time t.
St+h = stock price at time t+h.
C = call option price.
є = stock price change from time t to time t + h.
∆ = option delta.
Γ = option gamma.
Related information
A delta-hedged position is a position designed to earn the risk-free rate of interest and is used to offset the risk of an option position.
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G. Stolyarov II
Posted on 04/21/2008 at 10:04:40 AM
G. Stolyarov II
Posted on 04/18/2008 at 2:04:08 PM