Zakamouline Optimal Delta Hedging

Implementation of Optimal Hedging of Options with Transaction Costs by Valeri. I. Zakamouline.

Requirements

My other repo containing a BSM model implementation.

References

• Optimal Hedging of Options with Transaction Costs by Valeri. I. Zakamouline.
• Volatility Trading: 2nd Edition by Euan Sinclair.

Usage

• Obtaining hedgeband values at current spot price.

'''@Init Call & Put
Spot = 100
Strike = 100
DTE = 60
RFR = 5%
Volatility = 30%'''
call = BsmOption(False, 'C', 100, 100, 60, 0.05, sigma=0.3)
put = BsmOption(False, 'P', 100, 100, 60, 0.05, sigma=0.3)

#Init short straddle position
short_straddle = OptionPosition([call, put])

#Get hedgebands at current spot price
'''Position = short_straddle
Proportional transaction cost lambda where (tc = lambda * num_shares * spot) = 2%
Risk aversion parameter (higher results in tighter bands) = 1'''
up_band, down_band = hedgebands(short_straddle, 0.02, 1)

• Obtaining hedgebands for range of spot prices.

for i in range (0, 200)
    call = BsmOption(False, 'C', i, 100, 60, 0.05, sigma=0.3)
    put = BsmOption(False, 'P', i, 100, 60, 0.05, sigma=0.3)
    short_straddle = OptionPosition([call, put])
    up_band, down_band = hedgebands(short_straddle, 0.02, 1)

Interpretation

• If position delta breaches a band, you buy the requisite number of shares to bring delta just inside closest band. This is referred to as hedging to the band.
  • Eg: In the figure above, if an overnight gap brought your position to Δ = -0.70, you would hedge to the nearest band (down band) at Δ = -0.55 by purchasing 15 shares.