PRICING VULNERABLE AMERICAN PUT OPTIONS UNDER JUMP–DIFFUSION PROCESSES

2016 ◽  
Vol 31 (2) ◽  
pp. 121-138 ◽  
Author(s):  
Guanying Wang ◽  
Xingchun Wang ◽  
Zhongyi Liu
Keyword(s):  
Default Risk ◽  
Diffusion Processes ◽  
Compound Poisson Process ◽  
Jump Diffusion ◽  
Option Prices ◽  
Jump Diffusions ◽  
Put Options ◽  
Jump Diffusion Processes ◽  
American Put Options ◽  
American Put

This paper evaluates vulnerable American put options under jump–diffusion assumptions on the underlying asset and the assets of the counterparty. Sudden shocks on the asset prices are described as a compound Poisson process. Analytical pricing formulae of vulnerable European put options and vulnerable twice-exercisable European put options are derived. Employing the two-point Geske and Johnson method, we derive an approximate analytical pricing formula of vulnerable American put options under jump–diffusions. Numerical simulations are performed for investigating the impacts of jumps and default risk on option prices.

Optimal insurance control for insurers with jump-diffusion risk processes

2018 ◽  
Vol 13 (1) ◽  
pp. 198-213
Author(s):  
Linlin Tian ◽  
Lihua Bai
Keyword(s):  
Diffusion Processes ◽  
Compound Poisson Process ◽  
Linear Quadratic Regulator ◽  
Jump Diffusion ◽  
Analytic Solutions ◽  
Linear Quadratic ◽  
Discounted Cost ◽  
Optimal Insurance ◽  
Jump Diffusion Processes ◽  
Risk Processes

AbstractIn this paper, we model the surplus process as a compound Poisson process perturbed by diffusion and allow the insurer to ask its customers for input to minimize the distance from some prescribed target path and the total discounted cost on a fixed interval. The problem is reduced to a version of a linear quadratic regulator under jump-diffusion processes. It is treated using three methods: dynamic programming, completion of square and the stochastic maximum principle. The analytic solutions to the optimal control and the corresponding optimal value function are obtained.

scholarly journals Accuracy Tests Of American Put Valuation Models For Pharmaceutical Equity Options

2011 ◽  
Vol 6 (2) ◽  
Author(s):  
Yong H. Kim ◽  
Sangwoo Heo ◽  
Peter Cashel-Cordo ◽  
Yong S. Jang
Keyword(s):  
Option Prices ◽  
Equity Options ◽  
Forecasting Accuracy ◽  
Put Options ◽  
True Value ◽  
Black Scholes Model ◽  
American Put Options ◽  
Black Scholes ◽  
Variance Estimate ◽  
American Put

This study compares the performance of the Macmillan (1986), Barone-Adesi and Whaley (1987) MBAW model, Ju and Zhong (1999) MQuad model, Black-Scholes model and Put-Call Parity in pricing American put options of pharmaceutical companies. These are evaluated using actual option prices for three companies over 2000 to 2005, as opposed to the previous use of generated binomial option pricing data. We compare the forecasting accuracy by maturity, moneyness, and variance estimate. Contrary to Ju and Zhong (1999), we find that the MBAW outperforms the other models for at-the-money, and out-of-the-money options. The MQuad model performs best for in-the-money options. However, in this case both the MBAW and MQuad models estimates are very similar. Our results are consistent irrespective of option maturities and volatility estimates. These findings raise questions regarding the practice of using actual prices as the true value, compared to the previous results that use simulated prices.

scholarly journals Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes

2007 ◽  
Vol 44 (03) ◽  
pp. 713-731 ◽  
Author(s):  
Pavel V. Gapeev
Keyword(s):  
Optimal Stopping ◽  
Diffusion Processes ◽  
Free Boundary Problems ◽  
Compound Poisson Process ◽  
Jump Diffusion ◽  
Dimensional System ◽  
Closed Form Solutions ◽  
Jump Diffusion Processes ◽  
Lookback Options ◽  
Jump Diffusion Model

In this paper we present closed form solutions of some discounted optimal stopping problems for the maximum process in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problems to integro-differential free-boundary problems, where the normal-reflection and smooth-fit conditions may break down and the latter then replaced by the continuous-fit condition. We show that, under certain relationships on the parameters of the model, the optimal stopping boundary can be uniquely determined as a component of the solution of a two-dimensional system of nonlinear ordinary differential equations. The obtained results can be interpreted as pricing perpetual American lookback options with fixed and floating strikes in a jump-diffusion model.

scholarly journals A Finite Difference Scheme for Pricing American Put Options under Kou's Jump-Diffusion Model

2013 ◽  
Vol 2013 ◽  
pp. 1-11 ◽  
Author(s):  
Jian Huang ◽  
Zhongdi Cen ◽  
Anbo Le
Keyword(s):  
Finite Difference ◽  
Difference Scheme ◽  
Diffusion Model ◽  
Finite Difference Scheme ◽  
Jump Diffusion ◽  
Uniform Mesh ◽  
Put Options ◽  
American Put Options ◽  
Jump Diffusion Model ◽  
American Put

We present a stable finite difference scheme on a piecewise uniform mesh along with a penalty method for pricing American put options under Kou's jump-diffusion model. By adding a penalty term, the partial integrodifferential complementarity problem arising from pricing American put options under Kou's jump-diffusion model is transformed into a nonlinear parabolic integro-differential equation. Then a finite difference scheme is proposed to solve the penalized integrodifferential equation, which combines a central difference scheme on a piecewise uniform mesh with respect to the spatial variable with an implicit-explicit time stepping technique. This leads to the solution of problems with a tridiagonal M-matrix. It is proved that the difference scheme satisfies the early exercise constraint. Furthermore, it is proved that the scheme is oscillation-free and is second-order convergent with respect to the spatial variable. The numerical results support the theoretical results.

scholarly journals Discounted Optimal Stopping for Maxima of Some Jump-Diffusion Processes

2007 ◽  
Vol 44 (3) ◽  
pp. 713-731 ◽  
Author(s):  
Pavel V. Gapeev
Keyword(s):  
Optimal Stopping ◽  
Diffusion Processes ◽  
Free Boundary Problems ◽  
Compound Poisson Process ◽  
Jump Diffusion ◽  
Dimensional System ◽  
Closed Form Solutions ◽  
Jump Diffusion Processes ◽  
Lookback Options ◽  
Jump Diffusion Model

In this paper we present closed form solutions of some discounted optimal stopping problems for the maximum process in a model driven by a Brownian motion and a compound Poisson process with exponential jumps. The method of proof is based on reducing the initial problems to integro-differential free-boundary problems, where the normal-reflection and smooth-fit conditions may break down and the latter then replaced by the continuous-fit condition. We show that, under certain relationships on the parameters of the model, the optimal stopping boundary can be uniquely determined as a component of the solution of a two-dimensional system of nonlinear ordinary differential equations. The obtained results can be interpreted as pricing perpetual American lookback options with fixed and floating strikes in a jump-diffusion model.

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