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 rate
Discount factor
Exponential functions

Formulas

P(7,10) = exp(-f(7,10) * (10 - 7))
P(0,7) = P(0,10) / P(7,10)
Price of bond = (Face value / 100) * P(0,7)

Theorems

No-arbitrage condition in bond pricing

Suitable Grade Level

Undergraduate finance or economics