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> Option Rho ρ : a first attempt
 Option Rho ρ : a first attempt
Issued on December 05 2011 par Strategies-options.com
Rho ρ measures sensitivity to the riskfree rate
The riskfree rate r is one input to put into a pricing formula to get an option price.
An option, call or put, can't be worth more than underlying. For the same amount, one is able to buy an asset or to buy a call and to invest the rest of the cash in a cash account. A part of the option price would be funded by interest paid on the cash account. Thus, there is a relationship between option value and interest rates. I - Intuition : Portfolio A: 1 stock bought for $100 and a 1 year put strick at 100 bought for $3 This portfolio is today worth $103 Portfolio B: 1 year call struck at 100 that is worth $4, and $99 invested in a cash account that pay 1%/year. Those portfolio are alike : In 1 year if the spot is at $110, - portfolio A would be worth $110 (put = 0, asset = 110) - portfolio B would be worth $110 (call = 110 - 100 = 10, 99 -> 100 on the cash account) In 1 year if the spot is at $90, - portfolio A would be worth $100 (put = 100 - 90 = 10, asset = 90) - portfolio B would be worth $100 (call = 0, 99 -> 100 on the cash account) If interest rate rises, it becomes obvious that the call is easier to fund by the cash account. Demand and supply lead the call to be worth much more. Conversely, cash account becomes much more interesting when interest rates rise and for the same reason, puts and stock are sold. It leads to a less expensive price for the put. II - Graphs A 1 year call struck at 100 with a volatility at 30% on an underlying set at $100 :  The higher the interest rate, the higher the call value and the lower the put value A 1 year put struck at 100 with a volatility at 30% on an underlying set at $100 :  Next : Black & Scholes : A First Attempt Previous : Option Theta θ : A First Attempt OPTIONS 101 - INDEX OPTIONS 101 - CHAPTER I OPTIONS 101 - CHAPTER II OPTIONS 101 - CHAPTER III OPTIONS 101 - CHAPTER IV OPTIONS 101 - CHAPTER V OPTIONS 101 - CHAPTER VI Strategies-options.com |
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