1. Consider a market with one stock and one money market account, with the same assumptions on parameters (such as r, μ and σ²) 02) as in the derivation of the Black-Scholes formula given in class for European call option. Consider a contingent claim whose payoff depends on two dates T₁ and T2, with T₂ > T₁ > 0 and two numbers K₁ > 0 and K₂ > 0. The buyer of this contingent claim has the right to buy 1 share of the stock at time T₁ at price K₁. If the price of the stock at time T₁ is lower than or equal to K1, she then has a right to by the stock at price K2 at time T2. (She does not have the buying opportunity at time T2 if the price of the stock at time T₁ is strictly larger than K₁.) Find a formula for the current price (i.e. at time t = 0) of this contingent claim. The formula has to be explicit in the sense that one could feed into a computer program just like the Black-Scholes formula. The formula may contain integrals. It is not necessary to simplify the formula.

1. Consider a market with one stock and one money market account, with the same assumptions on parameters (such as r, μ and σ²) 02) as in the derivation of the Black-Scholes formula given in class for European call option. Consider a contingent claim whose payoff depends on two dates T₁ and T2, with T₂ > T₁ > 0 and two numbers K₁ > 0 and K₂ > 0. The buyer of this contingent claim has the right to buy 1 share of the stock at time T₁ at price K₁. If the price of the stock at time T₁ is lower than or equal to K1, she then has a right to by the stock at price K2 at time T2. (She does not have the buying opportunity at time T2 if the price of the stock at time T₁ is strictly larger than K₁.) Find a formula for the current price (i.e. at time t = 0) of this contingent claim. The formula has to be explicit in the sense that one could feed into a computer program just like the Black-Scholes formula. The formula may contain integrals. It is not necessary to simplify the formula.

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter2: Systems Of Linear Equations

Section2.4: Applications

Problem 28EQ

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