We propose to use the linearity-generating framework to accommodate the evidence of unspanned stochastic volatility: Variations in implied volatilities on interest-rate options such as caps and swaptions are independent of the variations on the interest rate term structure. Under this framework,...

The construction of martingales with given marginal distributions at given times is a recurrent problem in financial mathematics. From a theoretical point of view, this problem is well-known as necessary and sufficient conditions for the existence of such martingales have been described....

In this paper, we show that the calibration to an implied volatility surface and the pricing of contingent claims can be as simple in a jump-diffusion framework as in a diffusion one. Indeed, after defining the jump densities as those of diffusions sampled at independent and exponentially...

The theory of two price markets of Cherny and Madan (2010) yields closed forms for bid and ask prices. Defining profits as the difference between the mid quote and the risk neutral expectation and capital as difference between the ask and the bid price one obtains precise expressions for these...