We study both theoretically and empirically option prices on firms undergoing a cash merger offer. To estimate the merger's success probability, we use a Markov Chain Monte Carlo (MCMC) method using a state space representation of our model. Our estimated probability measure has significant...

The recently developed rough Bergomi (rBergomi) model is a rough fractional stochastic volatility (RFSV) model which can generate more realistic term structure of at-the-money volatility skews compared with other RFSV models. However, its non-Markovianity brings mathematical and computational...

This note examines a numerical approach for computing American option prices in the lognormal jump–diffusion context. The approach uses the known transition density of the process to build a discrete-time, homogenous Markov chain to approximate the target jump–diffusion process. Numerical...

This article presents a Markov chain framework to characterize the behavior of the CBOE Volatility Index (VIX index). Two possible regimes are considered: high volatility and low volatility. The specification accounts for deviations from normality and the existence of persistence in the...

The computation of the bilateral counterparty valuation adjustment for a credit default swap (CDS) contract is in effect the modeling of the default dependence among the investor, the protection seller, and the reference entity. We present a contagion model, where defaults of three parties are...

We consider the valuation of European quanto call options in an incomplete market where the domestic and foreign forward interest rates are allowed to exhibit regime shifts under the Heath–Jarrow–Morton (HJM) framework, and the foreign price dynamics is exogenously driven by a regime...

This paper considers a model where there is a single state variable that drives the state of the world and therefore the asset price behavior. This variable evolves according to a multi-state continuous time Markov chain, as the continuous time counterpart of the Hamilton (1989) model. It...

We consider two sequences of Markov chains inducing equivalent measures on the discrete path space. We establish conditions under which these two measures converge weakly to measures induced on the Wiener space by weak solutions of two SDEs, which are unique in the sense of probability law. We...

In this paper, which is a substantial extension of the earlier essay Björk (2001), we give an overview of some recent work on the geometric properties of the evolution of the forward rate curve in an arbitrage free bond market. The main problems to be discussed are as follows. 1. When is a...

In this paper we study a fairly general Wiener driven model for the term structure of forward prices. The model, under a fixed martingale measure, Q, consists of two infinite dimensional stochastic differential equations (SDEs). The first system is a standard HJM model for (forward) interest...