When you ask someone the following question: A currency has 5% interest rates (can be generalized to any security). The base currency (costs of funds) is 5%.The underlying moves up 1% a day for 22 days in a row. How do you compute volatility (Standard Deviation) for the PURPOSE of decision-making (option pricing)?
Almost everyone I’ve quizzed throughout my career answers: 0% volatility. Their spreadsheet functions using series of log returns also erroneously provide: 0% volatility.
The real answer is 16% annualized.
Why? STD = Sqrt[(E[X-E[x])^2] MAD =E[|X-E[x]|]
When you are facing an uncertain outcome you do not expect the mean return to be 1% a day. You simply expect 0% drift. Therefore you should not center volatility around the ex post drift but the ex ante one.
In other words, the options would produce the P/L of 0 volatility if and only if the drift is expected to be 1%
The classical anticipating-nonanticipating strategy. AN OPTION BREAKS EVEN AT 16% VOL (+- some adjustment) NOT 0.
A currency has 100% annual interest rates [paid daily]. Base currency is 5%. The exchange rate does not move for a month. What is volatility (monthly, annualized)? Easy…
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