By Daragh McInerney, Tomasz Zastawniak
ISBN-10: 1107002575
ISBN-13: 9781107002579
This quantity within the studying Mathematical Finance sequence moves simply the appropriate stability among mathematical rigour and useful program. present books at the demanding topic of stochastic rate of interest types are usually too complex for Master's scholars or fail to incorporate useful examples. Stochastic rates of interest covers functional subject matters similar to calibration, numerical implementation and version obstacles intimately. The authors supply a variety of routines and thoroughly selected examples to aid scholars gather the mandatory abilities to house rate of interest modelling in a real-world environment. furthermore, the book's web site at www.cambridge.org/9781107002579 offers ideas to all the workouts in addition to the pc code (and linked spreadsheets) for all numerical paintings, which permits scholars to ensure the implications.
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Sample text
The two key advantages of short-rate models are their general simplicity and the fact that they often lead to analytic formulae for bonds and associated vanilla options. The tractability of short-rate models means that the price of a given derivative can often be computed quickly, important in situations where a large number of securities need to be valued. Indeed, throughout this chapter, we focus on short-rate models that allow discount bonds to be priced in closed form. One-factor models assume that the entire interest rate term structure is driven by a one-dimensional Wiener process.
6) in the Vasi˘cek model. 2). 3 Note that, in both the Merton and Vasi˘cek models, bond prices can be written as B(t, T ) = e f (t,T )−g(t,T )r(t) , where f (t, T ) and g(t, T ) are deterministic functions. Models of this type are referred to as affine term structure models. The value of affine term structure models lies in their relative simplicity. 1), that is, if μ(t, r(t)) = γ(t)r(t) + δ(t), σ(t, r(t))2 = η(t)r(t) + (t), where the time-dependent functions are suitably well behaved, then the model is said to possess an affine term structure.
Indeed, throughout this chapter, we focus on short-rate models that allow discount bonds to be priced in closed form. One-factor models assume that the entire interest rate term structure is driven by a one-dimensional Wiener process. Such models are usually suitable when pricing securities that depend on a single rate only, but for more complex products which depend on two or more different rates we may need to move to a multi-factor model driven by multi-dimensional Brownian motion. In the final section we present one of the most popular multi-factor short-rate models, the two-factor Hull–White model.
Stochastic Interest Rates by Daragh McInerney, Tomasz Zastawniak
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