It is important to obtain fair option prices because it is useful to deliver a theoretical fair price of a certain option to provide traders with a rational basis that can be used to judge whether actual option prices in the marketplace are reasonable, and to help investors determine where to place bids and offers. Furthermore, cross field application such as Real Option Analysis must apply option pricing models. As a result, almost all expected value related applications will benefit from option pricing models.
Most modern option pricing models apply mathematical distributions to approximate underlying asset behavior and attempt to calculate the desired option price using close form formulas. However, limitations on current option pricing models also decline the use of mathematical option pricing models. For example, the limitations may be a) too many assumptions, b) mismatch between real payoff distributions and mathematical distributions, and c) lack of flexibility & limited application ranges.
In order to construct a new option pricing model, this study first observes actual payoff distributions from the real world. The empirical evidence based on observation of the actual payoff distribution suggests that the actual distribution of a stock index is time variant and cannot be described using mathematical distributions, meaning the approach of most options pricing models is ineffective. To optimize the pricing performance, this study first introduces a computational model for pricing European options via time variant distributions and then demonstrates its practical feasibility using actual payoff distributions.
This study solves two key issues in applying user defined distribution to options pricing. First, this study uses weighting factors to adjust the mean value of a none-risk-neutral distribution to
Second, this study scales the distribution to adjust its standard deviation to meet the needs associated with applying dynamic volatility to practical problems. Solving these two issues makes this computational model highly suitable for cross field applications where mathematical distribution cannot be used to obtain feasible solutions, particularly for situations involving time variant distributions.
Although the proposed computational method is practical for real world application, room still exists for improvement. First, the weighting factor rotating method used to adjust the value of the distribution means can be enhanced. This study assumes linearly changing weighting factors. Nonlinear modification methodologies require further study. Second, this study uses a simple method based on adjusting standard deviation that may not be able to deal with complex applications. Third, the computational method must be simplified before it can be applied to execution speed critical applications.
Reference
[1] E.K. Clemons (1991) Evaluating strategic investment in information system,
Communications of the ACM 34(1) : 22-36.
[2] B.L. Dos Santos (1991) Justifying Investment in new information technologies, Journal of
management information systems 7(4) : 71-89.
[3] F. Black and M. Scholes (1973) The pricing of options and corporate liabilities. Journal of
Political Economy 81(3): 637–59.
[4] M. Benaroch (2002) Managing information technology investment risk: a real options
perspective, Journal of management information systems 19(2) : 43 - 84.
[5] W.K. Chen (2001) Options: Theory, Practice and Application, Best-wise corp., 383-401 [6] J.O. Katz (2005) Advanced Option Pricing Models, Mc Graw Hill Corp., 52-56
[7] Stoll, Hans R. (1969) The relationship between put and call option prices, Journal of
Finance 23: 801-824.
[8] Cox J.C. and A. Ross (1976) The valuation of options for alternative stochastic processes.
Journal of Financial Economics 3: 145-166
[9] M. Joshi (2003) The Concepts and Practice of Mathematical Finance, Cambridge
publications, 17-18
[10] R.S. Johnson, C. Giaccotto (1995) Options and Futures, West publishing company, 207-208
[11] Whaley, E. Robert (1982) Valuation of American Call Options on Dividend-Paying
[12] R. Merton. (1973) Theory of rational option pricing, Bell Journal of Economics 4:
141-183.
[13] K. Amin, R. Jarrow (1992) Pricing Options on Risky Assets in a Stochastic Interest Rate
Economy. Mathematical Finance 2: 217-237.
[14] D.S. Bates (1996) Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in
Deutsche Mark Options, Review of Financial Studies 9: 69–107.
[15] D.S. Bates (1991) The Crash of '87: Was It Expected? The Evidence from Options Markets.
The Journal of Finance 46: 1009-1044.
[16] Madan, B. Dilip, P. Carr and Eric C. Chang (1998) The Variance Gamma Process and
Options Pricing. European Finance Review 2(1): 79-105.
[17] M. Rubinstein (1994) Implied binomial trees. Journal of Finance 49 : 771--818.
[18] A.S Yacine, A.W. Lo (1996) Nonparametric estimation of state-price densities implicit in
financial asset prices. Journal of Finance 52: 499-548.
[19] D. Bates (1996) Jumps and stochastic volatility: exchange rate processes implicit in
Deutsch mark options. Review of financial studies 9 : 69--107.
[20] Scott, O. Louis (1997) Pricing Stock Options in a Jump-Diffusion Model with Stochastic
Volatility and Interest Rates: Applications of Fourier Inversion Methods. Mathematical Finance 7: 345-358.
[21] B. Mandelbrot (1963) The Variation of Certain Speculative Prices, Journal of Business,
36, 394-419.
[22] L.C.G. Rogers (1997) Arbitrage from fractional Brownian motion, Mathematical Finance,
Vol. 7, No. 1, 95–105.
[23] R.C. Blattberg, N.J. Gonedes (1974) A comparison of the stable and student distributions as statistical models for stock prices, Journal of Business 47, 244-80.
[24] B. Nielsen, O. E. Stephard. (2001) Non-Gaussian Ornstein-Uhlenbeck based models and
some of their uses in financial economics (with discussion), J. Royal Stat. Soc.
63(2), ,pp.167-241
[25] P.K. Clark (1973) A subordinated stochastic process model with finite variance for speculative prices, Econometrica 41, pp.135-155.
[27] C.C. Heyde (2000) A risky asset model with strong dependence through fractal activity
time, Journal of Applied Probability 36, pp.1234-1239.
[28] Hull, J., A. White (1987) The pricing of options on asset with stochastic volatilities, Journal of Finance 42, , pp.281-300.
[29] R. Engle (1995) ARCH, Selected Readings., Oxford University Press, Oxford, U.K.
[30] J.P. Fouque, , G. Papanicolaou, K. R. Sircar (2000) Derivatives in Financial Market with
Stochastic Volatility, Cambridge University Press, Cambridge, U.K.
[31] D. Davydov, V. Linetsky (2001) The valuation and hedging of path-dependent options under the CEV process, Management Science 47, pp.949-956.
[32] S.L. Heston (1993) A closed-form solution for options with stochastic volatility with
applications to bond and currency options, The review of Financial studies, 6:2, pp.327-343.
[33] D. Duffie, J. Pan, K. Singleton (2000) Transform analysis and asset pricing for affine
jump-diffusions,. Ecomometrica 68(3), pp.1343-1376.
[34] S.G. Kou (2002) A jump-diffusion model for option pricing, Management Science 48:8,
pp.1086-1101.
[35] E. Derman, I. Kani (1994) Riding on a smile, RISK 7, pp.32-39.
[36] B. Dupire (2000) Pricing with a smile, RISK 7, pp.18-20.
[37] J.M. Hutchinson, A.W. Lo, and T. Poggio (1994) A nonparametric approach to Pricing and
[38] A. Carverhill, T.H.F. Cheuk (2003) Alternative Neural Network Approach for Option
Pricing and Hedging. Available at SSRN: http://ssrn.com/abstract=480562 or DOI:
10.2139/ssrn.480562
[39] G. Meissner, N. Kawano (2001) Capturing the volatility smile of options on high-tech
stocks: A combined GARCH-Neural network approach, Journal of economics and finance 25:
276-292.
[40] H.R. Stoll, R.E. Whaley (1990).The dynamics of stock index and stock index futures
returns. Journal of Financial and Quantitative Analysis, 25, 441-468.
[41] K. Chan (1992). A further analysis of the lead-lag relationship between the cash market
and stock index futures market. Review of Financial Studies, 5, 123-152.
[42] K.R. French, R. Roll (1986). Stock return variances: The arrival of information and the
reaction of traders. Journal of Financial Economics, 17, 5-26.
[43] S. Ross (1989) Information and volatility: The no-arbitrage martingale approach to
timing and resolution irrelevancy. Journal of Finance, 44, 1-17.
[44] I.G. Kawaller, P.D. Koch, T.W. Koch (1987) The Temporal Price Relationship between
S&P 500 Futures and the S&P 500 index. Journal of Finance, 42:1309-1329.
[45] K. Chan, K.C. Chan, G.A. Karolyi (1991) Intraday volatility in the stock index and stock
index futures markets. Review of Financial Studies, 4, 657-684.
[46] G. Koutmos, M. Tucker (1996). Temporal relationships and dynamic interactions
between spot and futures stock markets. Journal of Futures Markets, 16, 55-69.
[47] W.R. So, Y. Tse (2004) Price Discovery in the HANG SENG INDEX MARKETS: index,
futures, and the tracker fund. The Journal of Futures Markets. Hoboken, Sep 2004.Vol.24, Iss.
9; pg. 887
[48] H. Latane, R. Rendleman (1976) Standard deviation of stock price ratios implied in
option prices. Journal of Finance 31,369-381.
[49] D.P. Chiras, S. Manaster (1978) The information content of option prices and a test of
market efficiency. Journal of Financial Economics 6 (2/3), 213-234.
[50] L. Canina, S. Figlewski (1993). The informational content of implied volatility. Review
of Financial Studies 6, 659-681.
[51] T. Day, C. Lewis (1992) Stock market volatility and the information content of stock
index options. Journal of Econometrics 52, 267-287.
[52] C.G. Lamoureux, W. Lastrapes (1993) Forecasting stock return variance: towards
understanding stochastic implied volatility. Review of Financial Studies 6, 293-326.
[53] C.R. Harvey, R.E. Whaley (1992) Market volatility prediction and the efficiency of the
S&P 100 index option market, Journal of Financial Economics 31, 43-73.
[54] J. Fleming (1998) The quality of market volatility forecasts implied by S&P 100 index
option prices Journal of Empirical Finance vol. 5 pp. 317-345.
[55] Whaley, E. Robert (1982) Valuation of American Call Options on Dividend-Paying
Stocks: Empirical Tests. Journal of Financial Economics,10: 29-58.
[56] S. Beckers (1981) Standard Deviations Implied in Option Prices as Predictors of Future
Stock Price Variability, Journal of Banking and Finance, Vol. 5, No. 3, 1981, pp. 363-381.
[58] C.C. Sheng, H.Y. Chiu, A.P. Chen Using Computational Methodology to Price European
Options with Actual Payoff Distributions, Soft Computing, Online published February 2007 [59] H. Tanaka, S. Uejima, K. Asai (1982) Linear regression analysis with fuzzy regression
model, IEEE Trans. Systems Man Cybernet, 12, 903-907
[60] H. Tanaka, J. Watada (1988) Possibilistic linear systems and their application to the linear regression model, Fuzzy Sets and Systems, 27, 275-289
Analysis Based on Linear Programming, Fuzzy Set and Systems, 105, 429-436
[62] J.R. Yu, G.H. Tzeng, and H.L. Li (2001) General Fuzzy Piecewise Regression Analysis
with Automatic Change-Point Detection, Fuzzy Set and Systems, 119, 247-257
[63] R.F. Engle (1982) Autoregressive Conditional Heteroskedasticity with Estimates of the
Variance of United Kingdom Inflation, Econometrica, 50, 987-1007
[64] T. Bollerslev (1986) Generalized Autoregressive Conditional Heteroskedasticity, Journal
of Econometrics, 31, 307-327.
[65] I.G. Kawaller, P.D. Koch, and T.W. Koch (1987) The Temporal Price Relationship Between S&P 500 Futures and the S&P 500 Index,” Journal of Finance, 42, 1309-1329