45 research outputs found
Solving the dual Russian option problem by using change-of-measure arguments
We apply the change-of-measure arguments of Shepp and Shiryaev [38]to study the dual Russian option pricing problem proposed by Shepp and Shiryaev [39] as an optimal stopping problem for a one-dimensional diffusion process with reflection. We recall the solution to the associated free-boundary problem and give a solution to the resulting onedimensional optimal stopping problem by using the martingale approach of Beibel and Lerche [6] and [7]
American Step-Up and Step-Down Default Swaps under Levy Models
This paper studies the valuation of a class of default swaps with the
embedded option to switch to a different premium and notional principal anytime
prior to a credit event. These are early exercisable contracts that give the
protection buyer or seller the right to step-up, step-down, or cancel the swap
position. The pricing problem is formulated under a structural credit risk
model based on Levy processes. This leads to the analytic and numerical studies
of several optimal stopping problems subject to early termination due to
default. In a general spectrally negative Levy model, we rigorously derive the
optimal exercise strategy. This allows for instant computation of the credit
spread under various specifications. Numerical examples are provided to examine
the impacts of default risk and contractual features on the credit spread and
exercise strategy.Comment: 35 pages, 5 figure
Optimal Stopping in Levy Models, for Non-Monotone Discontinuous Payoffs
We give short proofs of general theorems about optimal entry and exit problems in Levy models, when payoff streams may have discontinuities and be non-monotone. As applications, we consider exit and entry problems in the theory of real options, and an entry problem with an
embedded option to exit
ADAPTIVE WEAK APPROXIMATION OF DIFFUSIONS WITH JUMPS
This work develops adaptive time stepping algorithms for the approximation of a functional of a diffusion with jumps based on a jump augmented Monte Carlo Euler–Maruyama method, which achieve a prescribed precision. The main result is the derivation of new expansions for the time discretization error, with computable leading order term in a posteriori form, which are based on stochastic flows and discrete dual backward functions. Combined with proper estimation of the statistical error, they lead to efficient and accurate computation of global error estimates, extending the results by A. Szepessy, R. Tempone, and G. E. Zouraris [Comm. Pure Appl. Math., 54 (2001), pp. 1169–1214]. Adaptive algorithms for either deterministic or trajectory-dependent time stepping are proposed. Numerical examples show the performance of the proposed error approximations and the adaptive schemes