Math Problem Statement

The forward rate f(t1,t2) of a bond, is the implicit interest rate in a future period between time t1 and t2. For example assuming continuous time returns, if the discount rate from period 0 to period t1 is: exp(-r+t), and from period 0 to t2( greater than t1) is: exp(-r t2), then, the forward rate f from t1 to t2 maintains the following no arbitrage relationship: exp(-r t1) exp( -f (t2-t1) = exp(r-t2). suppose we observe the prices of a 10 year zero coupon bond ( with a face value of $99.99), where P(t1,t2) means the price of the bond between t1 and t2, and a year - to 10 forward rate as follows: P(0,10)= $91,8758115000 and f(7,10) = 0.8815309830%. Calculate the price of a seven year zero coupon, with face value $97.8. Choose one option : 1) $92.5406. 2)$91.859. 3) $91.5565. 4) $92.2718

Solution

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Math Problem Analysis

Mathematical Concepts

Bond Pricing
Forward Rates
Exponential Functions
Continuous Compounding

Formulas

exp(-r t1) * exp(-f(t2 - t1)) = exp(-r t2)
P(7, 10) = exp(-f(7,10) * (10 - 7))
P(0, 7) = P(0, 10) / P(7, 10)
P(0, 7) = F * (P(0, 7) / 100)

Theorems

No-Arbitrage Condition

Suitable Grade Level

Undergraduate Finance or Economics