Leland's Formula for Volatility Adjustment
October 5, 2006
We would like to highlight an important issue regarding the impact of bid-ask spreads on the volatility of asset prices. Of late we have received a lot of queries in this area in our training sessions and it is something that derivatives traders in Asia need to worry about especially, if they are trading options on emerging market assets.
Bid-ask spreads, i.e. the liquidity in a certain asset market, affect the volatility of an asset price through the transaction cost. If you are trading an emerging market FX or bond option or options on stocks which display wide bid-ask spreads then you should adjust the volatility of the options using Lehland's formula (it is an important formula and once upon a time we knew it by heart!)
Lehland's formula states that long call and put positions (options) should be valued with an adjusted volatility of where:
And short positions in call and put options should be valued with an adjusted volatility of which is given by:
In the above formulas is the bid-ask spread or the transaction cost in percentage, is a small interval of time over with the portfolio is revised and is the vanilla volatility.
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