An Analytical Approximation for European Option Prices Under Stochastic Interest Rate Economy

2014 ◽  
Author(s):  
Hideharu Funahashi
Keyword(s):  
Interest Rate ◽  
Analytical Approximation ◽  
Stochastic Interest Rate ◽  
Option Prices ◽  
European Option ◽  
Stochastic Interest

AN ANALYTICAL APPROXIMATION FOR EUROPEAN OPTION PRICES UNDER STOCHASTIC INTEREST RATES

2015 ◽  
Vol 18 (04) ◽  
pp. 1550026 ◽  
Author(s):  
HIDEHARU FUNAHASHI
Keyword(s):  
Interest Rates ◽  
Analytical Approximation ◽  
Option Prices ◽  
European Option ◽  
Stochastic Interest Rates ◽  
Option Markets ◽  
Stochastic Nature ◽  
Volatility Models ◽  
Stochastic Interest ◽  
High Volatility

This paper extends the Wiener–Itô chaos expansion approach proposed by Funahashi & Kijima (2015) to an equity-interest-rate hybrid model for the pricing of European contingent claims with special emphasis on calibration to the option markets. Our model can capture the volatility skew and smile of option markets, as well as the stochastic nature of interest rates. Further, the proposed method is applicable to widely used option pricing models such as local volatility models (LVM), stochastic volatility models (SVM), and their combinations with the stochastic nature of interest rates; hence, it is suitable for practical purposes. Through numerical examples, we show that our approximation is quite accurate even for long-maturity and/or high-volatility cases.

European Option Pricing under Fractional Stochastic Interest Rate Model

2010 ◽  
Vol 171-172 ◽  
pp. 787-790
Author(s):  
Wen Li Huang ◽  
Gui Mei Liu ◽  
Sheng Hong Li ◽  
An Wang
Keyword(s):  
Brownian Motion ◽  
Interest Rate ◽  
Fractional Brownian Motion ◽  
Stock Price ◽  
Stochastic Interest Rate ◽  
European Option ◽  
European Option Pricing ◽  
Stochastic Interest ◽  
Pde Method ◽  
And Control

Under the assumption of stock price and interest rate obeying the stochastic differential equation driven by fractional Brownian motion, we establish the mathematical model for the financial market in fractional Brownian motion setting. Using the risk hedge technique, fractional stochastic analysis and PDE method, we obtain the general pricing formula for the European option with fractional stochastic interest rate. By choosing suitable Hurst index, we can calibrate the pricing model, so that the price can be used as the actual price of option and control the risk management

scholarly journals Mellin Transform Method for European Option Pricing with Hull-White Stochastic Interest Rate

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Ji-Hun Yoon
Keyword(s):  
Interest Rate ◽  
Option Pricing ◽  
Interest Rates ◽  
Mellin Transform ◽  
Stochastic Dynamics ◽  
Closed Form Solution ◽  
Stochastic Interest Rate ◽  
Option Prices ◽  
European Option Pricing ◽  
Stochastic Interest

Even though interest rates fluctuate randomly in the marketplace, many option-pricing models do not fully consider their stochastic nature owing to their generally limited impact on option prices. However, stochastic dynamics in stochastic interest rates may have a significant impact on option prices as we take account of issues of maturity, hedging, or stochastic volatility. In this paper, we derive a closed form solution for European options in Black-Scholes model with stochastic interest rate using Mellin transform techniques.

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