Delta Hedging PDF
Delta Hedging PDF
Delta Hedging PDF
Background on Fundamentals
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What is Delta?
Before considering Delta Hedging, lets first review
Delta
Definition: In options trading, Delta is the measure
of how the value of an option changes with respect
to changes in the value of the underlying contract
Typically noted by the Greek letter:
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What is Delta?
Delta (in absolute value, ignoring negative sign) can
also be taken as an approximation of the probability
that the option will finish in-the-money
All information contained within this document is confidential and proprietary to Risk Limited Corporation
All information contained within this document is confidential and proprietary to Risk Limited Corporation
All information contained within this document is confidential and proprietary to Risk Limited Corporation
Terminology
In trading jargon, option traders often drop the
decimal point in describing deltas
So a delta of 0.62 may be called 62
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Delta Neutral
Neutral in that the total delta of the portfolio
transactions is zero
Total delta position of the portfolio is the aggregate
(arithmetic sum) of the transaction deltas
Positions with offsetting positive and negative deltas
All information contained within this document is confidential and proprietary to Risk Limited Corporation
All information contained within this document is confidential and proprietary to Risk Limited Corporation
All information contained within this document is confidential and proprietary to Risk Limited Corporation
All information contained within this document is confidential and proprietary to Risk Limited Corporation
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All information contained within this document is confidential and proprietary to Risk Limited Corporation
Closed-form solution
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All information contained within this document is confidential and proprietary to Risk Limited Corporation
All information contained within this document is confidential and proprietary to Risk Limited Corporation
Model Assumptions
Fixed volatility and interest rate over the life of
the option being valued
Lognormal price distribution for underlying
contract
Known future price volatility of the underlying
contract for the life of option
Known future interest rate for the life of the
contract
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Model Assumptions
Realistic assumptions? Generally not
Certainly not for knowledge of future volatility and
interest rates
Fixed volatility and lognormal assumptions often not
valid
Tax consequences may vary depending on liquidation
timing and other trade factors, as well as a traders
unique tax considerations
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Model Assumptions
How big of an issue in valuation accuracy?
It depends
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Hedge Ratio
Note that Hedge Ratio is also at times used as the
term to describe risk management elements other
than Delta Hedges (e.g. the amount of an exposure
that has been hedged)
The Hedge Ratio (the delta) gives the appropriate
ratio of underlying contracts to options required to
maintain a neutral hedge
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All information contained within this document is confidential and proprietary to Risk Limited Corporation
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All information contained within this document is confidential and proprietary to Risk Limited Corporation
Arbitrage
Fair value (theoretical) vs. Market price
Multiple bets necessary to reach theoretical fair
value
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All information contained within this document is confidential and proprietary to Risk Limited Corporation
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All information contained within this document is confidential and proprietary to Risk Limited Corporation
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All information contained within this document is confidential and proprietary to Risk Limited Corporation
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All information contained within this document is confidential and proprietary to Risk Limited Corporation
Summary
Delta Hedging is a widely used technique for
managing option portfolios
Routinely used by professional traders
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All information contained within this document is confidential and proprietary to Risk Limited Corporation
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