Lecture 17

# Lecture 17 - Dividends If a stock pays dividends at a rate...

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Dividends If a stock pays dividends at a rate q, then we just reduce the initial price, S 0 , to S 0 e -qT , and then go ahead. This changes the Black-Scholes-Merton formula as well as the boundaries and put-call parity formulas. where now both d 1 and d 2 subtract q from r . Note that the Ke -rt does not change only the S 0 is discounted at (r q). The binomial tree formulas change to keep the expected return at (r q) instead of r. The Black-Scholes differential equation becomes where, again, S is discounted at (r q) but f is still multiplied by r not (r q). Options on Indices Now the formula σ and q are the average values for all of the underlying stocks in the index. The only index option that is American is the S&P 100 the rest are European. (Although there are flex options on some.) These index options can be used by portfolio managers to change their beta values or provide some insurance against particularly severe drops. For example, suppose a fund takes \$1000 from 100 investors and buys the S&P 100 index. There are different ways to guarantee the investors

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Lecture 17 - Dividends If a stock pays dividends at a rate...

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