Explain how when risk free interest rate increases, call value increases?

don't underestand.

also a bonus would be if you can refer me to a site you know of which explains many different items such as these.

thanks!

The answer by "raysor" was concise and accurate. I tend to be more long-winded which sometimes helps and sometimes doesn't.

One of the assumptions made by option pricing models is that on average the price of a stock will increase at the risk free interest rate. Another assumption is that the price distribution for stocks will be a bell shaped curve, a variation of a "normal distribution" known as a "log-normal distribution."

To keep things simple, assume a stock is selling for $100 per share and you are looking at a call option that expires in exactly one year. If the risk free interest rate is 5% the call will be priced assuming at expiration the stock will be over $105 half the time and under $105 half the time. If the risk free interest rate is 10% the call will be priced assuming at expiration the stock will be over $110 half the time and under $110 half the time. Since $110 is more than $105 the call option is worth more at 10% than 5%.

I'll continue with the same example to explain why the pricing model makes the assumption. If the interest rate was 10% the call and the put with a strike price of $110 would be about equal in price. That would mean you could buy the stock, sell the $110 call and buy the $110 put for a total of about $100 per share. At expiration the call would be assigned if the stock was above $110. If the stock was below $110 you could exercise the put. Either way you would have made $10 per share because you sold the stock for $10 more than you paid for it. That is the same amount you would have made if you had received 10% interest without ever having traded the stock or options. The combination of the long stock, long put option and short call option is known as a "conversion spread" and is considered a risk free arbitrage position.

If the price of the call and the put did not change when the risk free interest rate dropped to 5%, you could still make 10% with the conversion spread but you could only make 5% interest. Since no one is likely to choose to make 5% risk free when he could make 10% risk free, the market would have to adjust. Either the risk free interest rate would have to go up or the price of the options would have change to bring the risk free conversion spread return down from 10% to 5%.

<<<a bonus would be if you can refer me to a site you know of which explains many different items such as these.>>>

There are two sites I recommend, the CBOE Learning Center at

http://www.cboe.com/LearnCenter/default.aspx

and the OIC education site at

http://www.optionseducation.org/

but if you really want to understand option pricing I recommend the book "Option Volatility & Pricing" by Sheldon Natenberg.

Fundamentally if the money you earn for investing in an asset with zero risk of loosing your money increases then the price of all assets which carry a risk of loosing your money also increases. A call is the right to purchase a risky asset for a set price at a set time in the future.

The academic model for pricing options is the Blackâ€“Scholes. One of the variables in the equation is the risk free rate.

With a call option you are saying you will buy the underlying at some point in the future.The cost of doing that is calculated partly by interest rates (the future value of money) If interest rates go up it will be more expensive in the future.

For more info. about the greeks see investopedia.com

If you buy a call option it gives you the right to buy a stock at a certain value. The seller risks the chance that it will go a lot higher than the call's intrinsic value, and also it is somewhat like buying it on credit so if the interest rates rise, the call value tends to go up.

I don't know what you mean by 'bonus', but you may mean the call's premium in excess of it's intrinsic value.

A $50 call on a $ 51 stock has an intrinsic value of $ 1, but it will sell at maybe $ 2.00. If the stock is down to $ 50 when the call expires, the call expires worthless, but if the stock rises to $ 55 on the expiration date, the call has an intrinsic value of $ 4, but will lose the premium since that is the seller's fee for the risk of it going up which means he only gets $52.00 (the $ 50 strike price plus the money for the call).

look up the 'Greeks' with respect to call option values. when an option calculator calculates a call value, it also typically provides you with info referred to as the greeks: delta, gamma, rho, vega, and a few more.

these reflect the relationship b/w underlying factors and the call option value. In the case of risk free rates, the 'rho' is the number you're looking for. so if an option has a rho of 1, then if the risk free rate goes up by one percent, the value of the call option will increase by one unit of value as well. this is a VERY general example.

see this site for more info:

http://www.optiontradingpedia.com/free_option_greeks.htm

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