# Relationship between interest rate and option value

### Effect of Interest Rates on Options by express-leader.info

Options, being a form of derivative instrument, derives their value from their The "interest rate" referred to in relation to the prices of options is what is known as. Is there any relationship among F, S(t), t realized value of an uncertain asset ( the line is sloped). With interest rate options, the underlying. An option's value is made up of seven parts stock price, strike price, volatility, time to expiration, interest rates and dividends.

This is the main area where the model can skew the results. Stock Price If a call option allows you to buy a stock at a specified price in the future than the higher that price goes, the more the option will be worth.

Which option would have a higher value: A call option allows you to buy The Option Prophet sym: In this situation, our option value will be higher. Strike Price Strike price follows along the same lines as stock price. When we classify strikes, we do it as in-the-money, at-the-money or out-of-the-money. When a call option is in-the-money, it means the stock price is higher than the strike price.

### RHO: Why Interest Rates Effect Our Option Premiums | The Blue Collar Investor

When a call is out-of-the-money, the stock price is less than the strike price. On the flip side of that coin, a put option is in-the-money when the stock price is less than the strike price.

A put option is out-of-the-money when the stock price is higher than the strike price. Options that are in-the-money have a higher value compared to options that are out-of-the-money.

Type Of Option This is probably the easiest factor to understand. An option is either a put or a call, and the value of the option will change accordingly.

## RHO: How Do Interest Rates Affect Our Option Premiums?

A call option gives the holder the right to buy the underlying at a specified price within a specific time period.

A put option gives the holder the right to sell the underlying at a specified price within a specific time period. If you are long a call or short a put your option value increases as the market moves higher.

If you are long a put or short a call your option value increases as the market moves lower. Time To Expiration Options have a limited lifespan thus their value is affected by the passing of time. As the time to expiration increases the value of the option increases. As the time to expiration gets closer the value of the option begins to decrease. The value begins to rapidly decrease within the last thirty days of an option's life.

The more time an option has till expiration, the more time the option has to move around. Interest Rates Interest rates have a minimal effect on an option's value.

When interest rates rise a call option's value will also rise, and a put option's value will fall. Plus we will have the same reward potential for half the risk. Now we can take that extra cash and invest it elsewhere such as Treasury Bills.

### RHO: How Do Interest Rates Affect Our Option Premiums?

This would generate a guaranteed return on top of our investment in TOP. The higher the interest rate, the more attractive the second option becomes.

Thus, when interest rates go up, calls are a better investment, so their price also increases. On the flip side of that coin if we look at a long put versus a long call, we can see a disadvantage. We have two options when we want to play an underlying to the downside. You can short shares of the stock which would generate cash into the brokerage and allow us to earn interest on that cash.

You long a put which will cost you less money overall but not put extra cash into your brokerage that generates interest income. The higher the interest rate, the more attractive the first option becomes. So what exactly is this "interest rate" that influences the price of options? The first mistake most people make is assuming that it is the interest rate you get from putting your money in a bank that is referred to here.

## RHO: Why Interest Rates Effect Our Option Premiums

So we frequently get people asking how the price of options are affected if interest rates at the bank rises or falls. That is not the interest rate referred to here in options trading even though all interest rates tend to trend in the same direction over time. The "interest rate" referred to in relation to the prices of options is what is known as the "Risk Free Interest Rate". Now, what exactly is the "Risk Free Interest Rate"? It is the interest you can get from your money with no risk which also represents the "opportunity cost" of putting your money somewhere else.

By investing in another financial instrument such as Options or buying a stock, the stock trader or options trader is foregoing the risk free interest they can get on their money. The specific interest rate used for this purpose in the pricing of options is the interest rate on Treasury Bills or T-Bills. Treasury bills are US government bonds that represents risk free return on your money for the specific time frame covered by the various T-bills. The annualized continuously compounded rate on treasury bills is then taken into consideration in the Black Scholes Model for the calculation of theoretical options price as the options greek " Rho ".

Effect of Interest Rates on Call Options Call options premium rises when interest rate rises and falls when interest rate falls. Apart from the obvious fact that this is due to the interest rate component Rho changes in the Black Scholes Options Pricing Model formula, what is the real life justification for such an effect? There are a few different justifications for the higher call options premium when interest rate rises.

Bear in mind that the risk free interest rate is the opportunity cost of investing in other financial instruments such as stocks or options.

The higher the interest rate, the higher the opportunity cost of taking the money out of bonds and into those instruments. When interest rates are high, the opportunity cost of buying stocks becomes higher because investors are losing out more T-bills interest. That makes buying call options instead of the stocks more attractive. By buying call options instead of the stocks, investors can control the same amount of stock profits using just a small fraction of the money it takes to buy the actual stocks.

- Effect of Interest Rates on Options

This slightly higher demand for call options theoretically justifies for slightly higher call options premiums, all other factors remaining unchanged which again is never the case.

Over time, day T-bills increased to 0. The higher call options premium when interest rate rises is also additional compensation for the loss of additional interest incurred by options writers.

When an options writer sell you call options, they need to either have the same amount of stocks in inventory or have cash locked up in their account as margin. Either way, the options writer is denied the right to sell the stocks or reallocate the cash into those higher interest T-bills. This loss of interest by the seller is compensated by a higher options premium to be paid by the buyer of those call options. Effect of Interest Rates on Put Options Put options premium falls when interest rates rise and rises when interest rates falls.

So, whats the real life justification for such an effect? Put options are substitutes for shorting shares.

When an investor short shares, they get cash in their account which earns them interest. However, when they buy put options in order to speculate to downside, they don't get the extra cash in the bank, hence losing out on interest. This makes buying put options when interest rate rises less attractive than shorting the shares.

That lower demand theoretically justifies for the lower put options premium when interest rate rises, all other factors remaining unchanged. Conversely, when interest rate falls, shorting shares becomes less attractive than buying put options as the extra cash won't be making as much interest revenue, hence demand for put options rises along with its premium.

In fact, professional options traders substitute for shorting shares by taking what is known as a " Synthetic Short Stock Position " through the simultaneous purchase of put options and selling of call options.