We present an asymptotic solution for call options on zero-coupon bonds, assuming a stochastic process the price of bond, rather than interest rates in general. The bond incorporates dampening return volatility based maturity bond. derive PDE similar way to Black and Scholes. Using perturbation approach, we value option. result is interesting, as leading order terms are equivalent Black–Scholes...

The Trapezoidal Rule with second order Backward Difference Formula (TR-BDF2) time stepping method was applied to the Black-Scholes PDE for option pricing. It is proved that TR-BDF2 time stepping method is unconditionally stable, and compared to the usual Crank-Nicolson time stepping method, the TR-BDF2 shows fewer oscillations when computing the derivatives of the solution, which are important ...

We propose the use of a classical tool in PDE theory, the parametrix method, to build approximate solutions to generic parabolic models for pricing and hedging contingent claims. We obtain an expansion for the price of an option using as starting point the classical Black&Scholes formula. The approximation can be truncated to any number of terms and easily computable error measures are available.

The influence of the analytical properties of the Black-Scholes PDE formulation for American and Asian options on the quality of the numerical solution is discussed. It appears that numerical methods for PDEs are quite robust even when the mathematical formulation is not well posed.

We are concerned with a model for asset prices introduced by Koichiro Takaoka, which extends the well known Black-Scholes model. For the pricing of contingent claims, partial differential equation (PDE) is derived in a special case under the typical delta hedging strategy. We present an exact pricing formula by way of solving the equation.

We propose a few variations around a simple model in order to take into account the market impact of the option seller when hedging an option. This ”retro-action” mechanism turns the linear Black and Scholes PDE into a non-linear one. This model allows also to retrieve some earlier results of [9]. Numerical simulations are then performed.

Numerical Methods for Pricing Multi-Asset Options Yuwei Chen Master of Science Graduate Department of Computer Science University of Toronto 2017 We consider the pricing of two-asset European and American options by numerical Partial Differential Equation (PDE) methods, and compare the results with certain analytical formulae. Two cases of options are tested: exchange option and spread option. ...

In this thesis we present two methods for the pricing and hedging of cliquet options with global floor and/or cap within a Black-Scholes market model with fixed dividends and time dependent volatilities and interest rates. The first is a Fourier transform method giving integral formulas for the price and the greeks. A numerical integration scheme is proposed for the evaluation of these formulas...

In this paper we study partial differential equations (PDEs) that can be used to model value adjustments. Different adjustments denoted generally as xVA are nowadays added the risk-free financial derivative values and PDE approach allows their easy incorporation. The aim of is show how solve analytically in Black-Scholes setting get new semi-closed formulas compare widely standard approximation...