Abstract

A call option can be defined as a contract which gives its holder the purchase rights a financial security or commodity at the exercise price. On the other hand, put options could be defined as contracts which gives its holder the purchase rights a financial security or commodity at the exercise price. Usually call options and put options must be exercised within a given duration or period as agreed in the contract. Call options and put options are normally used to hedge risk by one party which is risk averse while the other party uses call options to make a profit by assuming the risk. Call options and put options can also be used for arbitrage purposes. Arbitrage refers to investors making riskless profits by taking advantage of price differentials. Investors who are risk averse prefer arbitrage. Opportunities for making arbitrage profit only exist if the put-call parity conditions are violated.

The theoretical value of a call option is given by the difference between the current market price of the commodity or security minus the exercise price. Call options are financial assets which are traded in active financial markets. Therefore, the prices of call options are influenced by forces of demand and supply.Factors that influence the price of a call option include; the stock price, exercise price, the risk free rate of return and stock volatility.

The stock price

The stock price is the current prevailing price of the stock in the spot market. A call option value is given by the difference of the stock price and the exercise price. Therefore, the higher the stock price, the higher will be the call option value. When the stock price is higher than exercise price, the value of the option will be positive what is referred to as in-the-money. However, when the stock price is lower than exercise price the value of the option will be negative what is referred to as out-of-the money. Buyers will be willing to pay a higher premium for a call option if the stock price is high and the converse is true if the stock price is low.

Exercise price

Exercise price is the specific price, determined at the inception of the call option, at which the stock will be purchased. Given the theoretical value of a call option is given by the difference between the current market price of the commodity or security minus the exercise price, it is logical to assume there is an inverse relationship between the value of a call option and its exercise price. The higher the exercise price of a call option the lower the value of the call option while the lower the exercise price of a call option the higher the value of the call option. A lower exercise price increases demand of a call option which exerts an upward pressure on its price.

Volatility

Volatility of the stock is a statistical tool that measures the intensity and frequency of the stock price fluctuations. Volatility only indicates the magnitude and not the direction of the stock price fluctuations. The higher the intensity of the stock price fluctuation, the higher the opportunity for the buyer and the higher the risk the writer faces. Therefore, the buyer must pay a higher premium to the seller as compensation for the higher risk. There are two measures of volatility; historical volatility and implied volatility. Historical volatility is computed on the basing on the stock price over a given period in the past. A higher historical volatility implies that the share price had sharp fluctuations. However, the price of option is based on the future. Given the fact that it is impossible to measure future volatility, market players use historical volatility to form an opinion about future volatility what is referred to as implied volatility. Assuming other factors constant, the higher the future volatility the higher, the call option price. In extreme cases, the volatility of the share price maybe zero. In this case, the theoretical value of the call option will be equal to the call option price.

Risk free interest rate

Risk free interest rate refers to the returns expected from a risk free investment. There is a direct relationship between risk free interest rate and call option price. This is because call options are risky investment. Therefore, the price of call options increases when the risk free interest rate increases because investors consider the higher returns they would make on riskless investments instead of buying the underlying stock. The writer of the call option also needs compensation for interest income forgone due to holding the underlying stock for the buyer instead of selling the stock and keeping the funds in interest bearing accounts. Normally call options usually have a positive ‘Rho’ hence their prices raise when the risk free rate of interest rises.

Call options and put options can also be used for arbitrage purposes. Arbitrage refers to investors making riskless profits by taking advantage of price differentials. Investors who are risk averse prefer arbitrage. Arbitrage opportunity normally exists if the put-call parity conditions have been violated.

Put-call Parity = C0 –S0 + Ee –rT

Where;

C0 is the call option price

S0 is share price = Exercise price – call price = 22.5 – 21.35

E is the exercise price

e is exponential

r is the interest rate

T is the time = 60 days/360 days = 1/6

1.15 – 21.35 + 22.5e-0.12*1/6 = 1.854

0.55 Therefore, the put-call parity is violated and an arbitrage opportunity exists

Buy a put option for $ 0.55

Sell a call option for $ 1.15

Buy a share for $ 21.35

Borrow 21.35 + 0.55 – 1.15 = $ 20.75 at the interest rate 12%

The arbitrage profit = 22.5 – 20.75e0.12*1/6 = 1.33

Conclusion

Call options are financial assets which are traded in active financial markets. Therefore, the prices of call options are influenced by forces of demand and supply. Factors that influence the price of a call option include; the stock price, exercise price, the risk free rate of return and stock volatility. Call options and put options can also be used for arbitrage purposes. Opportunities for making arbitrage profit only exist if the put-call parity conditions are violated

References

Brigham, E. F., & Ehrhardt, M. C. (2010). Financial Management Theory and Practice (13 ed.). London: Cengage Learning.

Kim, S. H., & Kim, S. H. (2006). Global corporate finance: text and cases (6, illustrated ed.). New York: John Wiley & Sons.

Kolb, R., & Overdahl, J. A. (2009). Financial Derivatives: Pricing and Risk Management (illustrated ed.). New York: John Wiley & Sons.

Shim, J. K., & Siegel, J. G. (2008). Financial Management (3, illustrated, revised ed.). New York: Barron's Educational Series.

Siddaiah, T. (2009). International Financial Management. Delhi: Pearson Education India.

A call option can be defined as a contract which gives its holder the purchase rights a financial security or commodity at the exercise price. On the other hand, put options could be defined as contracts which gives its holder the purchase rights a financial security or commodity at the exercise price. Usually call options and put options must be exercised within a given duration or period as agreed in the contract. Call options and put options are normally used to hedge risk by one party which is risk averse while the other party uses call options to make a profit by assuming the risk. Call options and put options can also be used for arbitrage purposes. Arbitrage refers to investors making riskless profits by taking advantage of price differentials. Investors who are risk averse prefer arbitrage. Opportunities for making arbitrage profit only exist if the put-call parity conditions are violated.

The theoretical value of a call option is given by the difference between the current market price of the commodity or security minus the exercise price. Call options are financial assets which are traded in active financial markets. Therefore, the prices of call options are influenced by forces of demand and supply.Factors that influence the price of a call option include; the stock price, exercise price, the risk free rate of return and stock volatility.

The stock price

The stock price is the current prevailing price of the stock in the spot market. A call option value is given by the difference of the stock price and the exercise price. Therefore, the higher the stock price, the higher will be the call option value. When the stock price is higher than exercise price, the value of the option will be positive what is referred to as in-the-money. However, when the stock price is lower than exercise price the value of the option will be negative what is referred to as out-of-the money. Buyers will be willing to pay a higher premium for a call option if the stock price is high and the converse is true if the stock price is low.

Exercise price

Exercise price is the specific price, determined at the inception of the call option, at which the stock will be purchased. Given the theoretical value of a call option is given by the difference between the current market price of the commodity or security minus the exercise price, it is logical to assume there is an inverse relationship between the value of a call option and its exercise price. The higher the exercise price of a call option the lower the value of the call option while the lower the exercise price of a call option the higher the value of the call option. A lower exercise price increases demand of a call option which exerts an upward pressure on its price.

Volatility

Volatility of the stock is a statistical tool that measures the intensity and frequency of the stock price fluctuations. Volatility only indicates the magnitude and not the direction of the stock price fluctuations. The higher the intensity of the stock price fluctuation, the higher the opportunity for the buyer and the higher the risk the writer faces. Therefore, the buyer must pay a higher premium to the seller as compensation for the higher risk. There are two measures of volatility; historical volatility and implied volatility. Historical volatility is computed on the basing on the stock price over a given period in the past. A higher historical volatility implies that the share price had sharp fluctuations. However, the price of option is based on the future. Given the fact that it is impossible to measure future volatility, market players use historical volatility to form an opinion about future volatility what is referred to as implied volatility. Assuming other factors constant, the higher the future volatility the higher, the call option price. In extreme cases, the volatility of the share price maybe zero. In this case, the theoretical value of the call option will be equal to the call option price.

Risk free interest rate

Risk free interest rate refers to the returns expected from a risk free investment. There is a direct relationship between risk free interest rate and call option price. This is because call options are risky investment. Therefore, the price of call options increases when the risk free interest rate increases because investors consider the higher returns they would make on riskless investments instead of buying the underlying stock. The writer of the call option also needs compensation for interest income forgone due to holding the underlying stock for the buyer instead of selling the stock and keeping the funds in interest bearing accounts. Normally call options usually have a positive ‘Rho’ hence their prices raise when the risk free rate of interest rises.

Call options and put options can also be used for arbitrage purposes. Arbitrage refers to investors making riskless profits by taking advantage of price differentials. Investors who are risk averse prefer arbitrage. Arbitrage opportunity normally exists if the put-call parity conditions have been violated.

Put-call Parity = C0 –S0 + Ee –rT

Where;

C0 is the call option price

S0 is share price = Exercise price – call price = 22.5 – 21.35

E is the exercise price

e is exponential

r is the interest rate

T is the time = 60 days/360 days = 1/6

1.15 – 21.35 + 22.5e-0.12*1/6 = 1.854

0.55 Therefore, the put-call parity is violated and an arbitrage opportunity exists

Buy a put option for $ 0.55

Sell a call option for $ 1.15

Buy a share for $ 21.35

Borrow 21.35 + 0.55 – 1.15 = $ 20.75 at the interest rate 12%

The arbitrage profit = 22.5 – 20.75e0.12*1/6 = 1.33

Conclusion

Call options are financial assets which are traded in active financial markets. Therefore, the prices of call options are influenced by forces of demand and supply. Factors that influence the price of a call option include; the stock price, exercise price, the risk free rate of return and stock volatility. Call options and put options can also be used for arbitrage purposes. Opportunities for making arbitrage profit only exist if the put-call parity conditions are violated

References

Brigham, E. F., & Ehrhardt, M. C. (2010). Financial Management Theory and Practice (13 ed.). London: Cengage Learning.

Kim, S. H., & Kim, S. H. (2006). Global corporate finance: text and cases (6, illustrated ed.). New York: John Wiley & Sons.

Kolb, R., & Overdahl, J. A. (2009). Financial Derivatives: Pricing and Risk Management (illustrated ed.). New York: John Wiley & Sons.

Shim, J. K., & Siegel, J. G. (2008). Financial Management (3, illustrated, revised ed.). New York: Barron's Educational Series.

Siddaiah, T. (2009). International Financial Management. Delhi: Pearson Education India.