International Journal of Theoretical and Applied Finance

In this paper, we investigate model-independent bounds for option prices given a set of market instruments. This super-replication problem can be written as a semi-infinite linear programing problem. As these super-replication prices can be large and the densities ℚ which achieve the upper bounds quite singular, we restrict ℚ to be close in the entropy sense to a prior probability measure at a next stage. This leads to our risk-neutral weighted Monte Carlo approach which is connected to a constrained convex problem. We explain how to solve efficiently these large-scale problems using a primal-dual interior-point algorithm within the cutting-plane method and a quasi-Newton algorithm. Various examples illustrate the efficiency of these algorithms and the large range of applicability.

We determine the price of digital double barrier options with an arbitrary number of barrier periods in the Black–Scholes model. This means that the barriers are active during some time intervals, but are switched off in between. As an application, we calculate the value of a structure floor for structured notes whose individual coupons are digital double barrier options. This value can also be approximated by the price of a corridor put.

We develop some simple simulation algorithms for CIR and Wishart processes. We investigate rigorously the square of a matrix valued Ornstein–Uhlenbeck process, the main idea being to split the generator and to reduce the problem to the simulation of the square of a matrix valued Ornstein–Uhlenbeck process to be added to a deterministic process. In this way, we provide a weak second-order scheme that requires only the simulation of i.i.d. Gaussian r.v.'s and simple matrix manipulations.

In this paper, we present algorithms to solve a complex system of partial integro-differential equations (PIDE's) of parabolic type. The system is motivated by applications in finance where the solution of the system gives the price of European options in a regime-switching jump diffusion model. The new algorithms are based on theoretical analysis in Florescu et al. (2012) where the proof of convergence of the algorithms is carried out. The problems are also solved using a more traditional approach, where the integral terms (but not the derivative terms) are treated explicitly. Another contribution of this work details a novel type of jump distribution. Empirical evidence suggests that this type of distribution may be more appropriate to model jumps as it makes them more clearly distinguishable from the signal variability.

Large-time asymptotics are established for the SABR model with β = 1, ρ ≤ 0 and β < 1, ρ = 0. We also compute large-time asymptotics for the constant elasticity of variance (CEV) model in the large-time, fixed-strike regime and a new large-time, large-strike regime, and for the uncorrelated CEV-Heston model. Finally, we translate these results into a large-time estimates for implied volatility using the recent work of Gao and Lee (2011) and Tehranchi (2009).

In this paper, a simple model for the evolution of the forward density of the future value of an asset is proposed. The model allows for a straightforward initial calibration to option prices and has dynamics that are consistent with empirical findings from option price data. The model is constructed with the aim of being both simple and realistic, and avoid the need for frequent re-calibration. The model prices of n options and a forward contract are expressed as time-varying functions of an (n + 1)-dimensional Brownian motion and it is investigated how the Brownian trajectory can be determined from the trajectories of the price processes. An approach based on particle filtering is presented for determining the location of the driving Brownian motion from option prices observed in discrete time. A simulation study and an empirical study of call options on the S&P 500 index illustrate that the model provides a good fit to option price data.

In this work, we present some numerical procedures for a wrong way risk model that can be used for credit value adjustment (CVA) calculations. We look at a model that uses a multi-factor Hull–White model for interest rates and a single-factor lognormal Black–Karasinski default intensity model for counterparty credit, where the default intensity driver is correlated with all interest rate drivers. We describe how a trinomial tree-based approach for implementing single factor short rate models by Hull and White (1994) can be modified and used to calibrate the intensity model to credit default swaps (CDSs) in the presence of correlation. We also provide approximate pricing methods for CDS options and single swap contingent CDS contracts. The latter methods could also be used for model calibration purposes subject to data availability.

We present new approximation formulas for local stochastic volatility models, possibly including Lévy jumps. Our main result is an expansion of the characteristic function, which is worked out in the Fourier space. Combined with standard Fourier methods, our result provides efficient and accurate formulas for the prices and the Greeks of plain vanilla options. We finally provide numerical results to illustrate the accuracy with real market data.