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Monotonicity of Option Prices Relative to Volatility

The Black-Scholes formula was the widely-used model for option pricing, this formula can be use to calculate the price of option by using current underlying asset prices, strike price, expiration time, volatility and interest rates. The European call option price from the model is a convex and increasing with respect to the initial underlying asset price. Assume underlying asset prices follow a generalized geometric Brownian motion, it is true that option prices increasing with respect to the constant interest rate and volatility, so that the volatility can be a very important factor in pricing option, if the volatility process £m(t) is constant (with £m(t) =£m for any t ) satisfying £m_1 ≤ £m(t) ≤ £m_2 for some constants £m_1 and £m_2 such that 0 ≤ £m_1 ≤ £m_2. Let C_i(t, S_t) be the price of the call at time t corresponding to the constant volatility £m_i (i = 1,2), we will derive that the price of call option at time 0 in the model with varying volatility belongs to the interval [C_1(0, S_0),C_2(0, S_0)].

Identiferoai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0718112-130733
Date18 July 2012
CreatorsCheng, Yu-Chen
ContributorsLai-Jiu LIN, Hong-Kun XU, Jen-Chih YAO, Ngai-Ching WONG
PublisherNSYSU
Source SetsNSYSU Electronic Thesis and Dissertation Archive
LanguageEnglish
Detected LanguageEnglish
Typetext
Formatapplication/pdf
Sourcehttp://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0718112-130733
Rightsunrestricted, Copyright information available at source archive

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