Explicit Bond Option and Swaption Formula in Heath-jarrow-morton One Factor Model
نویسنده
چکیده
We present an explicit formula for European options on coupon bearing bonds and swaptions in the Heath-Jarrow-Morton (HJM) one factor model with non-stochastic volatility. The formula extends the Jamshidian formula for zero-coupon bonds. We provide also an explicit way to compute the hedging ratio (∆) to hedge the option with its underlying.
منابع مشابه
Option Pricing in the Multidimensional Black-scholes-merton Market with Gaussian Heath-jarrow-morton Interest Rates: the Parsimonious and Consistent Hull-white Models of Vasicek and Nelson-siegel Type
unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract: An explicit state-price deflator for the multidimensional Black-Scholes-Merton market with a multiple factor Gaussian bond price dynamics is constructed. It immediately yields an extension of the Margrabe formula in this multiple risk economy. Restricting further the attention...
متن کاملA Class of Heath-jarrow-morton Term Structure Models with Stochastic Volatility
This paper considers a class of Heath-Jarrow-Morton term structure models with stochastic volatility. These models admit transformations to Markovian systems, and consequently lend themselves to well-established solution techniques for the bond and bond option prices. Solutions for certain special cases are obtained, and compared against their non-stochastic counterparts.
متن کاملMulti-Factor and Analytical Valuation of Treasury Bond Futures with an Embedded Quality Option∗
A closed-form pricing solution is proposed for the quality option embedded in Treasury bond futures contracts, under a multi-factor and Gaussian Heath, Jarrow, and Morton (1992) framework. Such an analytical solution can be obtained through a conditioning approximation, in the sense of Curran (1994) and Rogers and Shi (1995), or via a rank 1 approximation, following Brace and Musiela (1994). Mo...
متن کاملValuation of floating range notes in Lévy term structure
Turnbull (1995) as well as Navatte and Quittard-Pinon (1999) derived explicit pricing formulae for digital options and range notes in a one-factor Gaussian Heath-Jarrow-Morton (henceforth HJM) model. Nunes (2004) extended their results to a multifactor Gaussian HJM framework. In this paper, we generalize these results by providing explicit pricing solutions for digital options and range notes i...
متن کاملGuaranteed annuity conversion options and their valuation∗
In this chapter, we consider a theoretical model for the pricing and valuation of guaranteed annuity conversion options associated with certain unit-linked pension contracts in the UK. The valuation approach is based on the similarity between the payoff structure of the contract and a call option written on a coupon-bearing bond. The model makes use of a one-factor Heath-Jarrow-Morton framework...
متن کامل