In estimating the payoff of long strangles, we employ the terminal_stock_price function to project the final stock price for each iteration. However, I am perplexed by the use of a fixed sigma value instead of random values. Consequently, the estimations of the payoff for long strangles are limited to the sigma=0.4 environment, which lacks practicality since market volatility is not consistently fixed. Moreover, this approach unfairly influences the predictions of payoff for long strangles or straddles, as both strategies thrive in high-volatility environments where profits can be made. Therefore, would it be advisable to set sigma as a random value instead?
Hello Kevin,
You've raised a valid concern. In the current implementation, a fixed sigma value is used as an assumption. However, to make the code more realistic and representative of real-world scenarios, you can consider introducing randomness in the sigma values.
Within the Monte Carlo loop, before calling the 'long_strangle' function, sigma can be a random value sampled from a normal distribution. The mean for this distribution can be derived from mean volatility, which can be calculated either from historical price returns data or implied volatility. The standard deviation can be set as a multiple of the standard deviation of historical daily returns. The choice of this multiple depends on your risk appetite and how you want to model variations in volatility around the historical average. A value greater than 1 will represent higher variability, while a value less than 1 will represent lower variability in comparison to historical volatility.