The completion of real-asset markets by options.
The equation and financial mathematics. I
The existence of a weak solution and the uniqueness in law are assumed for the equation, the coefficients and being generally -progressive processes. Any weak solution is called a -stock price and Girsanov Theorem jointly with the DDS Theorem on time changed martingales are applied to establish the probability distribution of in in the special case of a diffusion volatility A martingale option pricing method is presented.
The Hull-White model and multiobjective calibration with consistent curves: empirical evidence.
The martingale method of shortfall risk minimization in a discrete time market
The shortfall risk minimization problem for the investor who hedges a contingent claim is studied. It is shown that in case the nonnegativity of the final wealth is not imposed, the optimal strategy in a finite market model is obtained by super-hedging a contingent claim connected with a martingale measure which is a solution of an auxiliary maximization problem.
The multi-dimensional super-replication problem under gamma constraints
The numerical valuation of options with underlying jumps.
The price of liquidity in constant leverage strategies.
The pricing of credit risky securities under stochastic interest rate model with default correlation
In this paper, we study the pricing of credit risky securities under a three-firms contagion model. The interacting default intensities not only depend on the defaults of other firms in the system, but also depend on the default-free interest rate which follows jump diffusion stochastic differential equation, which extends the previous three-firms models (see R. A. Jarrow and F. Yu (2001), S. Y. Leung and Y. K. Kwok (2005), A. Wang and Z. Ye (2011)). By using the method of change of measure and...
Thoughts about Selected Models for the Valuation of Real Options
This paper discusses option valuation logic and four selected methods for the valuation of real options in the light of their modeling choices. Two of the selected methods the Datar–Mathews method and the Fuzzy Pay-off Method represent later developments in real option valuation and the Black & Scholes formula and the Binomial model for option pricing the more established methods used in real option valuation. The goal of this paper is to understand the big picture of real option valuation models...
Transforming arithmetic Asian option PDE to the parabolic equation with constant coefficients.
Truncated variation, upward truncated variation and downward truncated variation of Brownian motion with drift-their mean value and their applications