To calculate the strike rate of the AUD put in relation to a 25.0% delta risk-reversal, we need to use the Black-Scholes formula for pricing options. However, the Black-Scholes formula requires the input of the strike price, which is what we are trying to find. Therefore, we need to use an iterative process to find the strike price that gives us a 25.0% delta.

Here are the steps:

1. Start with an initial guess for the strike price. A reasonable starting point might be the current spot rate.

2. Calculate the delta of the put option using the Black-Scholes formula. The formula for the delta of a put option is:

Delta = e^(-rtT) * N(-d1) - 1

where:
- e is the base of the natural logarithm
- rt is the terms currency interest rate
- T is the time to maturity
- N is the cumulative distribution function for a standard normal distribution
- d1 is given by the formula:

d1 = (ln(S/K) + (rc + sigma^2 / 2) * T) / (sigma * sqrt(T))

where:
- ln is the natural logarithm
- S is the spot rate
- K is the strike price
- rc is the risk-free rate
- sigma is the volatility

3. If the delta is not close enough to -0.25 (since we are dealing with a put option), adjust the strike price and go back to step 2.

4. Once the delta is close enough to -0.25, the corresponding strike price is the strike rate of the AUD put in relation to a 25.0% delta risk-reversal.

Please note that this process requires a numerical method such as the Newton-Raphson method or the bisection method to solve for the strike price. Also, the R/R adjustment is not used in this calculation.

Question

To calculate the strike rate of the AUD put in relation to a 25.0% delta risk-reversal, we need to use the Black-Scholes formula for pricing options. However, the Black-Scholes formula requires the input of the strike price, which is what we are trying to find. Therefore, we need to use an iterative process to find the strike price that gives us a 25.0% delta.

Here are the steps:

1. Start with an initial guess for the strike price. A reasonable starting point might be the current spot rate.

2. Calculate the delta of the put option using the Black-Scholes formula. The formula for the delta of a put option is:

Delta = e^(-rtT) * N(-d1) - 1

where:
   - e is the base of the natural logarithm
   - rt is the terms currency interest rate
   - T is the time to maturity
   - N is the cumulative distribution function for a standard normal distribution
   - d1 is given by the formula:

d1 = (ln(S/K) + (rc + sigma^2 / 2) * T) / (sigma * sqrt(T))

where:
     - ln is the natural logarithm
     - S is the spot rate
     - K is the strike price
     - rc is the risk-free rate
     - sigma is the volatility

3. If the delta is not close enough to -0.25 (since we are dealing with a put option), adjust the strike price and go back to step 2.

4. Once the delta is close enough to -0.25, the corresponding strike price is the strike rate of the AUD put in relation to a 25.0% delta risk-reversal.

Please note that this process requires a numerical method such as the Newton-Raphson method or the bisection method to solve for the strike price. Also, the R/R adjustment is not used in this calculation.

Knowee AI · Accepted Answer