We consider option pricing when dynamic portfolios are discretely rebalanced. The portfolio adjustments only occur after fixed relative variation of the stock price. The stock price follows a marked point process and the market is incomplete. We first characterize the equivalent martingale...

If calibrated to an observed term structure of interest rates that only covers a finite range of times-to-maturity an HJM-model of the term structure of interest rates will eventually die out in finite time as bonds reach maturity. This poses problems for the pricing and hedging of certain...

Option values are well-known to be the integral of a discounted transition density times a payoff function; this is just martingale pricing. It's usually done in 'S-space', where S is the terminal security price. But, for Levy processes the S-space transition densities are often very...

We generalize the Kou (2002) double exponential jump-diffusion model in two directions. First, we independently displace the two tails of the jump size distribution away from the origin. Second, we allow for each of the displaced tails to follow a gamma distribution with an integer-valued shape...

This paper extends the option pricing equations of Black and Scholes [1973. Journal of Political Economy 81, 637–654], Jarrow and Madan [1997. European Finance Review 1, 15–30] and Husmann and Stephan [2007. Journal of Futures Markets 27, 961–979]. In particular, we show that the length of...

In this paper, we provide a new dynamic asset pricing model for plain vanilla options and we discuss its ability to produce minimum mispricing errors on equity option books. Given the historical measure, the dynamics of assets are modeled by Garch-type models with generalized hyperbolic...

Let X be a seminmartingale and Teta the space of all predictable X-integrable processes teta such that integral tetat dX is inthe space S square of semimartingales. We consider the problem of approximating a given random variable H element of L square (P) by the sum of a constant c and a...

In this survey we discuss models with level-dependent and stochastic volatility from the viewpoint of erivative asset analysis. Both classes of models are generalisations of the classical Black-Scholes model; they have been developed in an effort to build models that are flexible enough to cope...

Consider a non-spanned security C_{T} in an incomplete market. We study the risk/return trade-offs generated if this security is sold for an arbitrage-free price Câ‚€ and then hedged. We consider recursive "one-period optimal" self-financing hedging strategies, a simple but tractable...