What Is Exchange Rate Volatility?

Volatility smiles refer to the relationship between the implied volatility of an option and the strike price. The volatility smile phenomenon is a common phenomenon in the options market and is of great significance in guiding options investment.

Volatility smile

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Volatility smiles refer to the relationship between the implied volatility of an option and the strike price. The volatility smile phenomenon is a common phenomenon in the options market and is of great significance in guiding options investment.
"Volatility smile" is an option that has the same expiration date and the underlying asset but has a different exercise price. The further the exercise price deviates from the spot price of the underlying asset, the greater the implied volatility. In empirical research, the implied volatility calculated by the traditional BS option pricing model presents a phenomenon called "volatility smile", that is, options with different maturity dates and underlying assets are executed at different prices. The further the exercise price of an option deviates from the spot price of the underlying asset, the greater its implied volatility.
Chinese name
Volatility smile
Foreign name
Volatility smiles
Implied Volatility in Options
(implied volatility)
Strike price
strike price
In-the-money options
in the money
Conventionally, the Black-Scholes pricing model assumes that the stock price volatility is constant, and generally underestimates the volatility of the subject matter. For stock options, the higher the exercise price, the smaller the volatility. When the exercise price approaches positive infinity, the call option price approaches 0, and the put option approaches positive infinity, and the volatility ratio approaches 0. For exchange rate options, the closer the exercise price is to the current price, the smaller the volatility.
The reason why it is called "volatility smile" is that the volatility of out-of-money and in-money options is higher than the volatility of at-money options, making the volatility The curve shows an upward half-moon shape that is low on both sides and high on the sides, that is, the shape of a smiling mouth, called a volatility smile.
Black-Scholes option pricing model
Volatility smile
-Some current theoretical developments: 1. Ilinski, Otto and Fedotov / Panayides introduced arbitrage opportunities into the Black-Scholes pricing model. The Ilinski and Otto models used an arbitrage opportunity X (following the Ornstein-Uhlenbeck process) to get a market 'average' option price. Fedotov / Panayides uses a more generalized goal; using bonds to simulate arbitrage opportunities, a more generalized formula is obtained.
2. Wilmott introduced stochastic volatility into the Black-Scholes pricing model. When S and t / T are constant, you will get a volatility smile (same as the BS result, but the BS assumes that the drift rate and volatility are fixed)

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