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# 152 the binomial formula and the black scholes model

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Unformatted text preview: odel The key assumption here is that the multiplicative movements change over time, and we can use the state price probability and do not on a period by period basis. Example The current stock price is 100. The multiplicative movements and are constant over time. The per period interest rate is 5%. The assumptions give the following evolution of the stock price ✟ ✟✟ ✟✟ ❍100 ❍ ❍❍ ❍ ✟✟ ✯ ✟ ✟ ❍❍ ✟ ❍❍ ✟ ❥ ❍✟ ❍❍ ✟ ✟✟ ✯ ✟ ✟✟ ❍❍ ❍❍ ❍ ❥ ❍ ✯ ✟ ✟✟ ✟ ✟✟ ❍❍ ❍ ❍❍ ❥ ❍ Let us price a two period European call option with exercise price The ﬁrst step is to ﬁnd option values at maturity, ✯ ✟ ✟✟ ✟ ✟ ✟ ✟✟ ✯ ✟ ❍❍ ✟✟ ❍❍ ✟ ❍❍ ✟✟ ✟ ❍ ❥ ❍ ✟ ❍❍ ✯ ✟ ✟✟ ❍❍ ✟ ❍ ✟✟ ❍❍ ❥ ❍ ✟✟ ❍❍ ❍❍ ❍ ❍❍ ❥ ❍ . : 15.2 The Binomial Formula and the Black Scholes Model 137 Given these payoﬀs at time 2, we use the state price probability to ﬁnd time 1 option prices We have now ca...
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## This document was uploaded on 02/15/2014 for the course BEM 103 at Caltech.

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