TIPS Options in the Jarrow-Yildirim model

An explicit pricing formula for inflation bond options is proposed in the Jarrow-Yildirim model. The formula resembles that for coupon bond options in the HJM model.Inflation bond option; Jarrow-Yildirim model

Swaptions: 1 price, 10 deltas, and ... 6 1/2 gammas.

In practice the option pricing models are calibrated to market prices of liquid instruments. Consequently for those instruments, all the models give the same price. But the computed risk can be widely different. The note proposes comparison on simple instruments (swaptions) on a simple risk measure (first and second order sensitivity to the underlying yield curve). The main paper conclusion is that the hedging widely (up to 10\% of the underlying risk) between the model, specially with their dynamic. The shape of the smile has also an impact but to a lesser extend.Swaption, delta, hedging, in-the-model, out-of-the-model sensitivity, models difference

Bonds futures and their options: more than the cheapest-to-deliver; quality option and marginning

Even if the name futures indicates a simple instrument, bond futures are complex. Several special features are embedded in the instrument. In particular the future is not written on one specific bond but on a basket of bonds, from which the short side can deliver the cheapest. This paper focuses on that feature, present in the main futures market, and its impact on the futures risk. A formula for the delivery option and the convexity adjustment due to the daily margining is proposed in the Gaussian HJM model. The approach is numerically very efficient and easy to implement. Based on this result a futures option formula is derived. The approach is similar to the one used for Canary swaptions.Bond future; option on bond futures; delivery option; marginning; Gaussian HJM model; explicit formula; numerical integration

Libor Market Model and Gaussian HJM explicit approaches to option on composition

The twin brothers Libor Market and Gaussian HJM models are investigated. A simple exotic option, floor on composition, is studied. The same explicit approach is used for both models. Using an approximation the LLM price is obtained without Monte Carlo simulation. The results of the approximation are very good, with an error well below the uncertainty due to the simulation. The appendices proves the existence of the (modified) normal and shifted log-normal LLM used in the pricing. The link of the latter with the Ho and Lee continuous time model is described.explicit formula, Libor market model, HJM model, shifted log-normal model, normal model, existence, option on composition

Explicit bond option and swaption formula in Heath-Jarrow-Morton one factor model

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 (Delta) to hedge the option with its underlying.Bond option, swaption, explicit formula, HJM model, one factor model, hedging

Parameter risk in the Black and Scholes model

We study parameter or estimation risk in the hedging of options. We suppose that the world is such that the price of an asset follows a stochastic differential equation. The only unknown is the (future) volatility of the asset. Options are priced and hedged according to the Black and Scholes formula. We describe the distribution of the profit and loss of the hedging activity when the volatility of the underlying is misestimated. A financial interpretation of the results is provided. Analytical bounds and numerical results for call, put, and portfolios complete our description.Black and Scholes model, option, parameter risk, profit distribution

Inflation bond option pricing in Jarrow-Yildirim model

Based on Jarrow-Yildirim model for inflation derivatives, this note propose an explicit formula for option on inflation bonds. The formula is similar to the one for coupon-bond option in the HJM model.Inflation bond option, Jarrow-Yildirim model

Comparisons of cashflow maps for value-at-risk

This article is devoted to the study cashflow maps used in the computation of value-at-risk (VaR). Properties and characteristics of the approaches found in the literature are presented and two new approaches are introduced. The goal of this paper is to study the quality of these maps. This is done by calculating the risk induced by the difference between the mapped cashflows and the original one.Value-at-risk, mapping, cashflows

CMS swaps in separable one-factor Gaussian LLM and HJM model

An approximation approach to Constant Maturity Swaps (CMS) pricing in the separable one-factor Gaussian LLM and HJM models is presented. The approximation used is a Taylor expansion on the swap rate as a function of a random variable which is intuitively similar to a (short) rate. This approach is different from the standard approach in CMS where the discounting is written as a function of the swap rate. The approximation is very efficient.CMS swap; LLM model; HJM model; one factor; approximation