Rho- Options Trading
“Greeks” is a term used in the options market that describes the different dimensions of risk involved in taking an options position. The reason for these variables to be called Greeks is that they are typically associated with Greek symbols. Each risk variable is a result of an imperfect assumption or relationship of the option with another underlying variable. Different Greek values like delta, gamma, theta, rho, and others are used by the traders to manage option portfolios.
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In finance, rho is a metric used to determine how sensitive an option is to risk-free rate changes. It is typically expressed in dollar amounts. It may also refer to the aggregated risk exposure to interest rate changes that exist for a book of several options positions. Long-term Equity Anticipation Securities options are far more sensitive to changes in interest rates than short-term equities.
What does Rho indicate?
Rho can be either negative or positive depending on whether the position is long or short and if it is a call or put option.
If all the other factors remain the same then the value of the option with positive rho will increase in interest rates rise and decrease with a fall in interest rates fall.
If all the other factors remain the same then the value of the option with negative rho will decrease with the increase in interest rates rise and increase with the fall in interest rates fall.
How is Rho Calculated?
where, d1 = [ln(S/K) + (r + σ2/2) * t] σ√t
d2 = d1 − σ√t
- S – Spot price
- K – Option strike price
- N – Normal cumulative distribution function
- r – Risk-free interest rate
- σ – Standard deviation
- t – time to option’s expiry
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Example of Rho
If there is a call option priced at $5.00 and has a rho of $0.50. if the risk-free interest rate increases by 0.5% then every 1% increase in the interest rate should increase the call option price by $0.50. therefore, the price of the option should increase by $0.25 ($0.5/1% x $0.50).so the new option price would be $5.25.
How it is used by Traders
Rho is really not that significant to the vast majority of traders but it has to do with the cost of carrying the position over time. Pricing models take into consideration the cost of capital which is used to offset the risk. For example, if an investor is looking to buy a deep-in-the-money put option with a delta of nearly -1 to make it delta-neutral then the market maker would have to buy 100 underlying securities. Buying the security would have the investor borrow money. If the interest rates increase the expense of carrying a long stock position increases. Thus, an investor buying this put will be willing to pay less if the interest rates rise to cover the expenses of carrying the position over time.
Although rho is an indispensable part of the Black Scholes Model it is regarded as the least used Greek option because for rho to have an impact on the option price the interest rates need to have drastic cases which is not the case usually.
Conclusion
It can be seen that rho is particularly useful only when the interest rate changes dramatically and this is the reason that it is not a part of the majority of options trading strategies.
Author -Sanjana Rau
About the author- Started my journey of self even when the odds were against me, keen observation, a cool temper, and sports worked the best for me.
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