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Solve the equation with final data V(T) = 1. This is the value of a coupon bond

Question:

Solve the equation

dV +K(t) = r(t)V, dt


with final data V(T) = 1. This is the value of a coupon bond when there is a known interest rate, r(t). What must we do if interest rates are not known in advance?

Transcribed Image Text:

dV +K(t) = r(t)V, dt

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To solve the given differential equation Vt Kt rt Vt Start by using the method of integrating factors multiply both sides of the equation by an integrating factor ...View the full answer


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Introduces Quantitative Finance

Introduces Quantitative Finance

ISBN: 978-0470319581

2nd edition

Authors: Paul Wilmott

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Bond valuation is the process of determining the worth of a bond. It is based on the present value of the bond\'s future cash flows, which include coupon payments and the return of the bond\'s face value (or \"principal\") at maturity. The discount rate used in the calculation is directly tied to prevailing interest rates, and a rise in interest rates will decrease the present value of the bond and thus lower its price. Conversely, a fall in interest rates will increase the present value of the bond and raise its price. Interest rates serve as a benchmark for determining the value of a bond, as they determine the discount rate used in the bond valuation calculation. The most commonly used measure of interest rates is the yield to maturity (YTM), which represents the internal rate of return of an investment in a bond if the investor holds the bond until maturity and receives all scheduled payments. Yield to maturity is a function of the coupon rate, the current market price of the bond, the face value of the bond, and the number of years remaining until maturity. By comparing the yield to maturity of a bond to prevailing market interest rates, an investor can assess the relative value of the bond.

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