2 inrealworldassetstradeinarangeofprices

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Unformatted text preview: d)][Cdd/(1+r)] = $2.46 Assume riskless rate is 3.9% for 1 period, so that compounded rate for 2 periods is 8%. (1+3.9%)2 = 1.08 C = [(1+r­d)/(u­d)][Cu/(1+r)] + [(u­1­r)/(u­d)][Cd/(1+r)] = [(1+r­d)/(u­d)][11.04/(1+r)] + [(u­1­r)/(u­d)][2.46/(1+r)] = $8.04 = $5 (intrinsic value) + $3.04 (time value) Option Pricing Option Pricing Note: The portfolio in the example is unrealistic: You cannot buy 0.75 of a share and the prices at expiry is more than 2 prices. However, it illustrates that investors can in principle create riskless portfolios by combining, ie, buying stocks and selling call options against such stocks. If call options are not priced as such, arbitrage opportunities will occur. Option Pricing Option Pricing “The Black­Scholes Option Pricing Model” Based on the premise that: 1. 2. In real world, assets trade in a range of prices, not only 2 as in the example. Creation of a risk­free portfolio. “The Black­Scholes Option Pricing Model” Formula V = P[N(d1)] – Xe­rt [N(d2)] d1 = ln(P/X) + [r + (σ2 /2 )]t σ( t) 1 /2 d2 = d1 ­ σ( t) 1 /2 “The Black­Scholes Option Pricing Model” Where: V = current value of a call option with time t until expiry P = current price of the underlying stock N(di) = probability that a deviation less...
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This document was uploaded on 04/02/2014.

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