OPTION VALUATION

The Black-Scholes pricing formula for call options

Introduction

Before or in the process of venturing into the global trading options, it is wise for traders to ensure that they have a better understanding of all the factors which assists in determining the value of an option (Poitras 438). Such factors include things like the cash dividends, volatility, expiration period, intrinsic and time value, and rates of interest to be paid. This is because they are the building blocks of the call value of stock in the financial market.

Moreover, there still exist various options pricing model which makes use of the above parameters in determining the fair market value of the option. Black-Scholes pricing model is one of these models which are widely used. In many ways, these options are perceived just like any other form of investment. This due to the fact that an investor needs to first understand all that determines their respective prices so as to take advantage of the market.

Basically, in using the Black-Scholes formula to find the value of a call option on the respective stock, the outcomes are to be dependent on the two parts of the model. This is then to mean that as much as the model is used in determining the call options available, what is noted is that the first part of the model SN(d1) is assists in multiplying the price of the commodities by their respective change in the call premium in respect to the changes which underlies the price. This then implies that in computing the variables, what is obtained is the expected return or benefit whilst purchasing the underlying outright. Similarly, in calculating the call option of the stocks, the next part of the model N(d2)Ke^(-rt), it is noted that it offers the current value of paying the exercise price of the stocks upon its expiration. The reason for this is because mostly the model is only applicable to the European options which are typically exercisable only on their expiration day (Benninga et al 307). Thus, in calculating the call option of the stocks, it indicates that the result is computed through taking the difference between these two parts.

Regardless of the above considerations, the computations which involves in the above variables are somehow intimidating or complicated. This then implies that that in making such calculations, there is no need of ensuring that investors and traders have a diversified knowledge in applying the modeling in their own strategies. In the above discussion, the options which is available for traders is the accessing various online calculators although they boast robust options in pricing the values.

As much as the main drivers of an option’s price are concerned, the current stock price should be regarded as being fairly obvious. The general movement of the stock prices up and down shows that it has a direct, though not equal, effect on the option price too. With the increase in the prices of the stocks, the more likely the price of the call options is to increase although the price of the put option will decrease. In case the prices of the stock decrease, it will mean that the reverse will most probably happen to the price of the calls or the puts. This equally indicates that the intrinsic value is mainly the value which any option will have in case it was to be exercised today (M & F.S 153). This then will remain to be the amount through which the strike price of any option is contained in the money. From the entire calculations, it shows the portion of the price of the option which is not lost because of the passage of time. This the indicates that the call or put option is obtained as;

Call option intrinsic value = the current price of the underlying stock\’s – the call strike price

Put option intrinsic value = the price of the put strike – the current price of the underlying stock\’s

In the long-run, the intrinsic value which is to be obtained for any of the option will reflect the effective financial advantage which will arise from the instant exercise of that option hence making it to be an option’s minimum value (M & F.S 154). The options which trades at out of money or at the money do will not have any intrinsic value.

Nonetheless, with the computations done, we can say that there exists a profound relationship between the call option value and the changes in each variable. With time value, it is usually the amount through which the option’s price exceeds the intrinsic value. This then indicates that it will be directly related to the amount of time such an option will have until it expires and the stock’s volatility. This is obtained as;

            Time value = option price – intrinsic value

Therefore, the more the time the option will be having before it expires, the greater its chances in ending up in the money. Although this component of an option expires exponentially, its actual derivation for any option is a fairly complex equation. The general rules is that as option will end up losing 1/3 of its entire value during its first half and 2/3 in the second of its whole life.  This makes it to be a significant concept for any security investor since the closer he or she gets to the expiration, the higher the chance of moving in the underlying securities which of course impacts the price of such an option (Albanese et al 321).

Additionally, although volatility is difficult to quantify, the effect it has is that it is a subjective. This is to imply that it will assist in determining the possible extent of the future moves which underlies the stock. Statistically, 2/3 of the entire occurrences of the price of stock would happen within plus or minus one of the standard deviation of the movement of stock over the set time. As a result, volatility looks back in time for the purpose of showing the extent at which the market has been volatile. In return, this will assist the options investors in determining the exercise price which is more appropriate to select for a certain strategy that might have in mind. Moreover, it will assist in setting the current price of the existing option as well as helping the option players in assessing the potential of the option trade. This is to say that the relationship of this parameter has is that it measures all the options the traders will be expecting in the future hence the implied volatility (Zhang 401). Seemingly, it is the indicator of the present sentiment of the stock or financial market. This will reflected in the option’s price thus aiding traders in assessing the future volatility of both the stock and option based on the existing option prices. Conversely the table below indicates the effects of these relationships that come as a result of computing the results of the stocks (Albanese et al 322). What is to be noted is that the user ought to input the entire five variable i.e. stock prices, time, volatility as well as the risk free interest rate to be met at the end.

If this variable increases	The Value of a Call Option
Stock Price	decrease
Exercise price	increase
Volatility	decrease
Time to expiration	increase
Interest rate	decrease

 

To sum up, any stock investors who will be interested in making use of the options so as to capture the potential move in the stock ought to have a better knowledge of how the options are priced. In addition to the principal price of the stock, the main determinants of the option’s price are mainly its intrinsic value- that is the amount at which the strike price of any option arrived at will be in-the-money as well as its corresponding time value.  Furthermore, time value will be related to the amount of time which will be remaining for such an option to expire and the option’s volatility. In addition to that, volatility is of a particular rate of interest to a stock in the sense that it wishes to use options so as to gain an added advantage (Janakiramanan 401). Acknowledging the existing and current volatility which is contained in the price of any particular option is important for any potential investor who desires to take the advantage of the stock price movement.

 

 

Work cited

Benninga, Simon, and Benjamin Czaczkes. Financial Modeling. Cambridge, Mass: MIT Press, 2000. Internet resource

Monetary and Financial Statistics: Compilation Guide. Washington. D.C: International Monetary Fund, 2008. Internet resource.

Albanese, Claudio, and Guiseppe Campolieti. Advanced Derivatives Pricing and Risk Management: Theory, Tools and Hands-on Programming Application. Asterdam: Elsevier, 2006. Print.

Janakiramanan, Sundaram. Derivatives and Risk Management. Chennai: Pearson/Dorling Kindersley, 2011. Internet resource.

Zhang, Peter G. Exotic Options: A Guide to the Second Generation Options. Singapore [u.a.: World Scientific, 1998. Print.

Poitras, Geoffrey. Risk Management, Speculation, and Derivative Securities. Amsterdam: Academic Press, 2002. Internet resource.