Options are instruments that give the holder the right, but not an obligation, to buy or sell an asset by a certain date for a certain price. Options can be bought or sold on a variety of assets like stocks, foreign currency, indexes, and futures. A call option gives the holder the right to buy the underlying asset and a put option gives the right to sell. The price at which the option is exercised is called the exercise price or strike price. The date by/at which the option can be exercised is called the expiration date/maturity date. American options can be exercised at any time up to maturity. European options can only be exercised at the expiration date. The option price is the price paid by the holder to the writer for buying an option to buy/sell one share of stock. Used properly, options provide the holders with an opportunity of making considerable profit with reduced or limited risks. They also require lesser initial investment than a direct purchase of stock would. Hence they are a very popular tool among investors. However, they may also cause considerable loss. Hence, the traders want to know what to expect of the market, whether an option is over-priced or under-priced, whether to buy or sell. They make their decisions based on their own experience and the information available to them, and with the help of mathematical or simulation models. Models of option pricing help them to determine the appropriate price for trading the option in the market. In fact, option trading took off only after the development of the Black-Scholes-Merton model of option pricing in 1973. The importance of correctly pricing options lies in the fact that option trading would become purely speculative in the absence of these models.
[...] Figure Model error The model mean squared error comes out to be 0.29 Scope For future works: Figure 5 shows that the square of the difference between the model output and the real option price is less than 1 in most places and reaches a maximum of only This leads us to conclude that the modeling approach described in this report can be employed to estimate option prices with reasonable accuracy. However, even though the model follows real market option prices with a mean squared error of only we see that it constantly over-estimates the market price. [...]
[...] This Paper describes an option pricing method that takes into account the decisionmaking process of the market players and hence, simulates the supply-demand dynamics of the options market for the Philips stock trading at the Amsterdam Stock Exchange, from 2nd Jan'06 to 17th March'06 for a strike price of 26.5 Euros. OR Based Valuation Approaches: For valuation of stocks, Capital assets Pricing Model ) which stipulates that return on any security is risk free rate plus a linear premium added as a function of Beta of security is the widely used approach. [...]
[...] (Eq By repeatedly simulating movements in the stock price, and hence the option price, a complete probability distribution of the option price is obtained. Artificial neural networks attempt to identify the underlying relationships in a set of data by using a process that mimics the way the human brain operates. They have the ability to adapt to changing input so that the network produces the best possible result without the need to redesign the output criteria. Amilon(2003) examines whether neural networks can be used to find a call option pricing formula better corresponding to market prices than the Black-Scholes formula using Black-Scholes models with historical and implied volatility as benchmarks. [...]
[...] Thus we use system dynamics modeling to depict the dynamics around the static pricing as stock and option using OR based equilibrium model. Unified CAPM- BS-System Dynamics model may serve to integrate the expectations of various market players in a dynamic market environment. Feedback structure provided into the model may serve to capture the dynamics oscillations, major peaks and valleys we witness in Stock and options market. Understanding such dynamics shall help to design regulatory polices that will stabilize the market and contribute to the optimal investment allocations to real industry sectors System Dynamics: System Dynamics philosophy rests on a belief that behavior of system is principally caused by the structure of the system and the policies embedded in system operations. [...]
[...] Investors' option buying rate Investors' option selling rate + - + Change in option price + Option price Ratio of option price to intrinsic value Intrinsic value Strike Price + Stock Price + - Ratio of actual price to BS price + BS Price Figure Causal loop diagram for Investors' buying & selling decisions Speculators The speculators are concerned with quick gains from the market. Thus their trading strategies are driven by the current price of the option rather than whether the option is over-priced or under-priced. [...]
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