The Valuation of Interest Rate Derivative Securities by Jeroen F. J. De Munnik

By Jeroen F. J. De Munnik

This e-book offers a close evaluate and type of different techniques to valuing rate of interest established securities.

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Additional resources for The Valuation of Interest Rate Derivative Securities (Routledge New Advances in Economics, 1)

Sample text

This section will show that in the current model there does exist a unique probability measure such that the stochastic process of the longterm maturity bond PL(t, TL) in terms of the value of the short-term maturity bond PS(t, TS) is a martingale. After this, the exact Modelling bond prices 43 values will be derived of European call and put options with maturity TS written on the discount bond PL(t, TL), and some of the properties of these valuation formulas will be discussed. 7) with and The following theorem asserts the existence of a unique equivalent probability measure under which the relative price process martingale.

As in the previous example, the initial and final trading dates are zero and one, respectively, and , for all n=0, 1, 2, 3,… . Investors have the the trading dates are opportunity to invest in a money market account or stock with corresponding price processes S1={S1(t), 0 ≤ t ≤ 1} and S2={S2(t), 0 ≤ t ≤ 1}, respectively. The initial value of the stock is one and without loss of generality, it can be assumed that interest rates are deterministic and zero, such that S1(t)=1 for all 0 ≤ t ≤ 1. 37) The probability of ruin during the interval [t0, t1] is p=Pr(inf{t: S2(t) = 1+1/b}).

Arbitrage opportunities and the valuation of contingent claims 17 The stochastic process of the value of trading strategies , is defined accordingly and this multi-period economy will be referred to as the relative multi-period economy. 7 There exists an arbitrage opportunity of the first type in the multi-period economy if and only if there exists an arbitrage opportunity of the first type in the corresponding multi-period economy, in which prices are expressed in terms of the value of the locally riskless money market account.

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