Hi guys, I am looking some advice on a simple delta hedging strategy and tying up the end results to Volatility skew.
I am testing a strategy on options which are delta hedged daily using futures and analyse the Average PnL across 5000 Simulations. I am running this for 4 options (100, 95, 90, 85 Calls) of same maturity and same IVs. Spot starts at 100 and is simulated at 0% Rfr for a 3 year period. For each simulation , i have considered the IVs for all 4 options same as the realised vol of that simulation.( Zero skew and IV = RV). Simulation is done assuming GBM form "dS = rf * S * dt + sigma * S * dW"
PnL for each simulation is given as below :
PnL(i) = Final Option Price(i) + Delta Hedging MTM(i) - Initial Option Price ; where i = ith simulation. PnL(1) = PnL across 1st path.
So, i get a pnl strip for each of the Call options.
Based on the data from the above exercise, i have a few observations and doubts that i would like your views on :
Observation 1: Expected Value of the Pnl(average of pnl across 5000 paths) for 100 Call is greater than expected value of the PnL for lower strike calls at a particular realized vol.
Doubt : Why is the expected pnl of such a strategy(delta hedging daily) dependent on the strike of the option. Fundamentally a delta hedged portfolio is considered to grow at a constant rate , and shouldn't it be same across any option for a particular maturity ? Is path dependency and gamma profile a reason for this.
Observation 2: Expected Value of the Pnl for 95 Call @ 19% = Expected Value of the Pnl for 100 Call @ 18%. As i increase the simulation vol, a low strike Call's average comes comes closer to 100 Call average pnl @ 18%. In the attachment, i have highlighted in yellow where Expected value of each options is close to that of 100 Call.
Doubt : Can there be a financial/economic sense to this observation ? Can this difference of 1% between 95 Call and 100 Call be termed as Vol Skew ? Or am i just overthinking it ?
Please let me know if you need more information about this exercise or if you think anything is flawed in the process. Thanks a lot !!
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Skew estimation using a delta hedging strategy on Equity options
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Re: Skew estimation using a delta hedging strategy on Equity options
Take a look at this
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Re: Skew estimation using a delta hedging strategy on Equity options
Suppose you rebalance every [$]\Delta t[$]. As [$]\Delta t \rightarrow 0[$], all your PnL's should go to zero, or you have an error. I would check that.