An analytical option pricing formula for mean-reverting asset with time-dependent parameter

2021 ◽  
Vol 63 ◽  
pp. 178-202
Author(s):  
Piyapoom Nonsoong ◽  
Khamron Mekchay ◽  
Sanae Rujivan
Keyword(s):  
Option Pricing ◽  
Option Price ◽  
Time Dependent ◽  
Initial Time ◽  
Agricultural Commodity ◽  
Time Integral ◽  
Long Run ◽  
Black Scholes ◽  
Dependent Parameter ◽  
Pricing Formula

We present an analytical option pricing formula for the European options, in which the price dynamics of a risky asset follows a mean-reverting process with a time-dependent parameter. The process can be adapted to describe a seasonal variation in price such as in agricultural commodity markets. An analytical solution is derived based on the solution of a partial differential equation, which shows that a European option price can be decomposed into two terms: the payoff of the option at the initial time and the time-integral over the lifetime of the option driven by a time-dependent parameter. Finally, results obtained from the formula have been compared with Monte Carlo simulations and a Black–Scholes-type formula under various kinds of long-run mean functions, and some examples of option price behaviours have been provided. doi:10.1017/S1446181121000262  

AN ANALYTICAL OPTION PRICING FORMULA FOR MEAN-REVERTING ASSET WITH TIME-DEPENDENT PARAMETER

2021 ◽  
Vol 63 (2) ◽  
pp. 178-202
Author(s):  
P. NONSOONG ◽  
K. MEKCHAY ◽  
S. RUJIVAN
Keyword(s):  
Option Pricing ◽  
Option Price ◽  
Time Dependent ◽  
Initial Time ◽  
Agricultural Commodity ◽  
Time Integral ◽  
Long Run ◽  
Black Scholes ◽  
Dependent Parameter ◽  
Pricing Formula

AbstractWe present an analytical option pricing formula for the European options, in which the price dynamics of a risky asset follows a mean-reverting process with a time-dependent parameter. The process can be adapted to describe a seasonal variation in price such as in agricultural commodity markets. An analytical solution is derived based on the solution of a partial differential equation, which shows that a European option price can be decomposed into two terms: the payoff of the option at the initial time and the time-integral over the lifetime of the option driven by a time-dependent parameter. Finally, results obtained from the formula have been compared with Monte Carlo simulations and a Black–Scholes-type formula under various kinds of long-run mean functions, and some examples of option price behaviours have been provided.

scholarly journals Perturbation Approach in the Dynamic Buckling of a Model Structure with a Cubic-quintic Nonlinearity Subjected to an Explicitly Time Dependent Slowly Varying Load

2019 ◽  
pp. 1-19
Author(s):  
A. M. Ette ◽  
I. U. Udo-Akpan ◽  
J. U. Chukwuchekwa ◽  
A. C. Osuji ◽  
M. F. Noah
Keyword(s):  
Perturbation Technique ◽  
Dynamic Buckling ◽  
Buckling Load ◽  
Time Dependent ◽  
Initial Time ◽  
Perturbation Approach ◽  
Elastic Model ◽  
Model Structure ◽  
Regular Perturbation ◽  
Long Run

This investigation is concerned with analytically determining the dynamic buckling load of an imperfect cubic-quintic nonlinear elastic model structure struck by an explicitly time-dependent but slowly varying load that is continuously decreasing in magnitude. A multi-timing regular perturbation technique in asymptotic procedures is utilized to analyze the problem. The result shows that the dynamic buckling load depends, among other things, on the first derivative of the load function evaluated at the initial time. In the long run, the dynamic buckling load is related to its static equivalent, and that relationship is independent of the imperfection parameter. Thus, once any of the two buckling loads is known, then the other can easily be evaluated using this relationship.

scholarly journals Nonparametric Estimation of Fractional Option Pricing Model

2020 ◽  
Vol 2020 ◽  
pp. 1-8
Author(s):  
Qing Li ◽  
Songlin Liu ◽  
Misi Zhou
Keyword(s):  
Option Pricing ◽  
Stock Exchange ◽  
Option Price ◽  
Integral Function ◽  
The State ◽  
Pricing Model ◽  
State Price ◽  
Black Scholes ◽  
Option Pricing Model ◽  
State Price Density

The establishment of the fractional Black–Scholes option pricing model is under a major condition with the normal distribution for the state price density (SPD) function. However, the fractional Brownian motion is deemed to not be martingale with a long memory effect of the underlying asset, so that the estimation of the state price density (SPD) function is far from simple. This paper proposes a convenient approach to get the fractional option pricing model by changing variables. Further, the option price is transformed as the integral function of the cumulative density function (CDF), so it is not necessary to estimate the distribution function individually by complex approaches. Finally, it encourages to estimate the fractional option pricing model by the way of nonparametric regression and makes empirical analysis with the traded 50 ETF option data in Shanghai Stock Exchange (SSE).

Abstract: Option Valuation Models–Some Implications of Parameter Estimation

1977 ◽  
Vol 12 (4) ◽  
pp. 667-667
Author(s):  
P. P. Boyle ◽  
A. L. Ananthanarayan
Keyword(s):  
Parameter Estimation ◽  
Option Pricing ◽  
Stock Prices ◽  
Unbiased Estimate ◽  
Estimation Error ◽  
Option Price ◽  
Nonlinear Function ◽  
Option Valuation ◽  
Black Scholes ◽  
Parameter Values

The Black-Scholes option pricing formula assumes that the variance of the return on the underlying stock is known with certainty. In practice an estimate of the variance, based on a sample of historical stock prices, is used. The estimation error in the variance induces error in the option price. Since the option price is a nonlinear function of the variance, an unbiased estimate of the variance does not produce an unbiased estimate of the option price. For reasonable parameter values, it is shown that the magnitude of the bias is not large.

scholarly journals Valuing Coca-Cola And PepsiCo Options Using The Black-Scholes Option Pricing Model And Data Downloads From The Internet

2012 ◽  
Vol 8 (6) ◽  
pp. 559-564
Author(s):  
John C. Gardner ◽  
Carl B. McGowan Jr
Keyword(s):  
Option Pricing ◽  
Stock Price ◽  
Option Price ◽  
Option Prices ◽  
Pricing Model ◽  
Black Scholes ◽  
Option Pricing Model ◽  
Risk Free Rate ◽  
Daily Returns ◽  
Free Rate

In this paper, we demonstrate how to collect the data and compute the actual value of Black-Scholes Option Pricing Model call option prices for Coca-Cola and PepsiCo.The data for the current stock price and option price are taken from Yahoo Finance and the daily returns variance is computed from daily prices.The time to maturity is computed as the number of days remaining for the stock option.The risk-free rate is obtained from the U.S. Treasury website.

scholarly journals LONG MEMORY STOCHASTIC VOLATILITY IN OPTION PRICING

2005 ◽  
Vol 08 (03) ◽  
pp. 381-392 ◽  
Author(s):  
SERGEI FEDOTOV ◽  
ABBY TAN
Keyword(s):  
Option Pricing ◽  
Stochastic Volatility ◽  
Long Memory ◽  
Option Price ◽  
Long Range Dependence ◽  
Asymptotic Equation ◽  
Random Deviation ◽  
Starting Point ◽  
Black Scholes ◽  
Different Time Scales

The aim of this paper is to present a stochastic model that accounts for the effects of a long-memory in volatility on option pricing. The starting point is the stochastic Black–Scholes equation involving volatility with long-range dependence. We define the stochastic option price as a sum of classical Black–Scholes price and random deviation describing the risk from the random volatility. By using the fact that the option price and random volatility change on different time scales, we derive the asymptotic equation for this deviation involving fractional Brownian motion. The solution to this equation allows us to find the pricing bands for options.

AN APPLICATION OF MELLIN TRANSFORM TECHNIQUES TO A BLACK–SCHOLES EQUATION PROBLEM

2007 ◽  
Vol 05 (01) ◽  
pp. 51-66 ◽  
Author(s):  
MARIANITO R. RODRIGO ◽  
ROGEMAR S. MAMON
Keyword(s):  
Existence And Uniqueness ◽  
Mellin Transform ◽  
Formal Solution ◽  
Option Price ◽  
Contingent Claims ◽  
Time Dependent ◽  
European Option ◽  
Equation Problem ◽  
Black Scholes Model ◽  
Black Scholes

In this article, we use a Mellin transform approach to prove the existence and uniqueness of the price of a European option under the framework of a Black–Scholes model with time-dependent coefficients. The formal solution is rigorously shown to be a classical solution under quite general European contingent claims. Specifically, these include claims that are bounded and continuous, and claims whose difference with some given but arbitrary polynomial is bounded and continuous. We derive a maximum principle and use it to prove uniqueness of the option price. An extension of the put-call parity which relates the aforementioned two classes of claims is also given.

Sign in / Sign up

Export Citation Format

Share Document