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  • Rho of a portfolio of options is the rate of change of its value with respect to changes in the interest rate
  • Rho = , where Π is the value of the portfolio, and r is the rate of interest
    • For European options on non dividend paying stocks, we have;
    • Rho (call) = KTe-rTN(d2), where the symbols carry their usual meanings
    • Also, Rho (put) = -KTe-rTN(-d2), the symbols carrying their usual meanings


  • Traders may combine naked and covered positions to evolve a stop-loss strategy
    • Stop loss strategy is impractical given the realities of trade and transaction costs involved
  • Delta hedging is an improvement
    • Involves that delta of the portfolio is maintained at zero
    • Requires frequent rebalancing as delta change
    • Dynamic hedging strategy
  • Hedging can also be attempted with respect to changes in:
    • Time (theta)
    • Option delta itself (Gamma)
    • Volatility (Vega)
    • Interest rate (Rho)
  • In addition to option Greeks, traders also rely on scenario analysis
  • Involves evaluating the option value for simultaneous changes in:
    • Time (Theta)
    • Volatility (Vega)
    • Interest rate (Rho)
    • Other factors


A stock trading at $20 has call options available on it with exercise prices $18 and $20. For $1 increase in the stock price how will the delta of the two options change? Choose the most appropriate answer. Change in deltas for the two options are denoted by d Δ18 and d Δ20.

  1. 18 < dΔ20
  2. 18 > dΔ20
  3. 18 = dΔ20
  4. 18 > dΔ20 and d Δ20 = 0




Which of the following statements is true regarding options’ Greeks?

  1. Theta tends to be large and positive for at-the-money options
  2. Gamma is greatest for in-the-money options with long times remaining to expiration
  3. Vega is greatest for at-the-money options with long times remaining to expiration
  4. Delta of deep in-the-money put options tends towards +1

Vega is the rate of change in the price of an option with respect to changes in the volatility of the underlying asset. Vega is greatest for at-the-money options with long times remaining to expiration




Which of the following statements is false?

  1. European-styled call and put options are most affected by changes in Vega when they are at the money
  2. The delta of a European-styled put option on an underlying stock would move towards zero as the price of the underlying stock rises
  3. The gamma of an at-the-money European-styled option tends to increase as the remaining maturity of the option decreases
  4. Compared to an at-the-money European-styled call option, an out-of-the money European option with the same strike price and remaining maturity would have a greater negative value for theta

Theta is large and negative for an at–the-money European-styled option, whilst theta is close to zero
when the price for the underlying stock is very low. Therefore the theta for an out-of the–money European styled call option would have a lower negative value compared to that of an at-the-money European-styled call option



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