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Lecture 11 Options on Other Assets

# Lecture 11 Options on Other Assets - L ectu re 11(Ch15&16 O...

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Lecture 11: (Ch15&16) Options on Other Assets Index options o Extension of results for European options on non-dividend-paying stock to European options on a stock paying a known dividend yield o Portfolio insurance Currency options Futures options Index Options The index options are settled in cash rather than by delivering the securities underlying the index. This means that upon exercise of the option, the holder of a call option receives S-X in cash and the writer of the call pays this amount in cash. Similarly, the holder of a put option receives X-S in cash and the writer of the option pays this amount in cash. Valuation of Index Options Extension of results from European options on non-dividend-paying stock to European options on a stock paying a known dividend yield Similar to the way of taking care of cash dividend [S 0 -PV(D)], when valuing a European option on a stock paying a known dividend yield at rate q, we reduce the current stock price from S 0 to S 0 e -q(T-t) and then value the option as though the stock pays no dividends. Replacing S 0 by S 0 e -q(T-t) in the B-S formulas given in (13.20) and (13.21), we have prices for call and put index options as

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If we assume that the value of stock index follows a risk-neutral process of: dS = ( r q ) Sdt + σ Sdz o where q is defined as a known dividend yield then the prices of European call & put options are: Example Question Calculate the value of a three-month at-the-money European call option on a stock index when the index is at 250, the risk-free interest rate is 10% per annum, the volatility of the index is 18% per annum, and the dividend yield on the index is 3% per annum.
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Lecture 11 Options on Other Assets - L ectu re 11(Ch15&16 O...

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