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Unformatted text preview: 280 4 Interest Rate Derivative Securities r = ( u w ) . Therefore the equation for any convertible bond is V t + 1 2 2 S 2 2 V S 2 + Sw 2 V Sr + 1 2 w 2 2 V r 2 + ( rS D ( S, t )) V S + ( u w ) V r rV + kZ = 0 . In this equation, only the market price of risk for the interest rate needs to be given. 26. Formulate the twofactor convertible couponpaying bond problem as a linear complementarity problem. Solution : Because for any derivative securities dependent on S, r, T and paying coupons with a rate k , the partial differential equation is V t + 1 2 2 S 2 2 V S 2 + Sw 2 V Sr + 1 2 w 2 2 V r 2 +( r D ) S V S + ( u w ) V r rV + kZ = 0 and the constraint and the payoff for convertible bonds are V ( S, r, t ) nS, and V ( S, r, T ) = max( nS, Z ) . Therefore the linear complementarity problem for the twofactor convert ible bond is V t + L S r V + kZ ( V nS ) = 0 , S, r l r r u , t T, V t + L S r V + kZ , S, r l r r u , t T, V nS , S, r l r r u , t T, V ( S, r, T ) = max( nS, Z ) nS, S, r l r r u , where L S r = 1 2 2...
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This note was uploaded on 02/11/2010 for the course MATH 6203 taught by Professor Zhu during the Spring '10 term at University of North Carolina Wilmington.
 Spring '10
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