why c=p=0.4 vol S (t)^.5

where does this come from? black schole model?

please show.

Finance Solution: A straddle includes long positions in both a call option and a put option with the same strike price K and maturity date T on the same stock. The payoff of a long straddle is SYK. So a straddle may be used to bet on large stock price moves. In practice, a straddle is also used as a trading strategy for making bets on volatility. If an investor believes that the realized (future) volatility should be much higher than the implied volatility of call and put options, he or she will purchase a strad fincestion of volatility. If the investor purchases an at-the-money straddle, both the call and the put options have the price cp0.4,S, where i is the implied volatility. If the realized volatility r>j, both options are finderyalued. When the market prices converge to the prices with the realized volatility, both the call and the put will become more valuable Although initially a straddle with an at-the-money call and an at-the-money put (K=S) has a delta close to 0 , as the stock price moves away from the strike price, the delta is no longer close to 0 and the investor is exposed to stock price movements. So a straddle is not a pure bet on stock volatility. For a pure bet on volatility, it is better to use volatility swaps or variance swaps. 11 For example, a variance swap pays N(r2Kvar), where N is the notional value, r2 is the realized variance and Kvar is the strike for the variance. Finance Solution: A straddle includes long positions in both a call option and a put option with the same strike price K and maturity date T on the same stock. The payoff of a long straddle is SYK. So a straddle may be used to bet on large stock price moves. In practice, a straddle is also used as a trading strategy for making bets on volatility. If an investor believes that the realized (future) volatility should be much higher than the implied volatility of call and put options, he or she will purchase a strad fincestion of volatility. If the investor purchases an at-the-money straddle, both the call and the put options have the price cp0.4,S, where i is the implied volatility. If the realized volatility r>j, both options are finderyalued. When the market prices converge to the prices with the realized volatility, both the call and the put will become more valuable Although initially a straddle with an at-the-money call and an at-the-money put (K=S) has a delta close to 0 , as the stock price moves away from the strike price, the delta is no longer close to 0 and the investor is exposed to stock price movements. So a straddle is not a pure bet on stock volatility. For a pure bet on volatility, it is better to use volatility swaps or variance swaps. 11 For example, a variance swap pays N(r2Kvar), where N is the notional value, r2 is the realized variance and Kvar is the strike for the variance