The stochastic-alpha-beta-rho (SABR) model introduced by Hagan et al. (2002) provides a popular vehicle to model the implied volatilities in the interest rate and foreign exchange markets. To exclude arbitrage opportunities, we need to specify an absorbing boundary at zero for this model, which...

The stochastic-alpha-beta-rho (SABR) model is widely used by practitioners in interest rate and foreign exchange markets. The probability of hitting zero sheds light on the arbitrage-free small strike implied volatility of the SABR model, and the survival probability is also closely related to...

This paper shows that a small-time Hermite expansion is feasible for multivariate diffusions. By introducing an innovative quasi-Lamperti transform, which unitizes the diffusion matrix at the initial time, we derive explicit recursive formulas for the expansion coefficients of transition...

In this paper, by adopting a quasi-Lamperti transform unitizing the process’ diffusion matrix at the initial time, we provide a new explicit recursive formula to compute the expansion coefficients for the pathwise Taylor expansion method of Li (2013). The quasi-Lamperti transform also allows...

The stochastic-alpha-beta-rho (SABR) model is widely used in fixed income and foreign exchange markets as a benchmark. The underlying process may hit zero with a positive probability and therefore an absorbing boundary at zero should be specified to avoid arbitrage opportunities. However, a...

Convertible bonds are hybrid securities that embody the characteristics of both straight bonds and equities. The conflict of interests between bondholders and shareholders affects the security prices significantly. In this paper, we investigate how to use a non-zero-sum game framework to model...

One of the important issues in behavioral analysis is that the time consistency property is lost due to the distortion in performance probability. The standard approach in performance optimization, the dynamic programming, fails to work in this area. In this paper, we propose to use an...

We study optimal effort and compensation in a continuous-time model with three-sided moral hazard and cost synergies. One agent exerts initial effort to start the project; the other two agents exert ongoing effort to manage it. The project generates cash flow at a fixed rate over its lifespan;...

This supplementary material for "Asymptotics for the Survival Probability of Time-Inhomogeneous Diffusion Processes" contains (i) some facts related to the normal density and distribution functions (Section 1), which are used in the calculation of explicit formulas in Equation (19) (Section 2);...