Managing investment and liquidity risks for derivatives within a market impact perspective

  • Received November 2, 2017;
    Accepted December 6, 2017;
    Published December 27, 2017
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  • Article Info
    Volume 8 2017, Issue #1, pp. 59-73

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This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License

The recent period has experienced many instances when market volatility suddenly increased even when there were no well-known fundamental catalysts, as illustrated by the short-lived but sharp transitions from low volatility to high volatility, as many in the last six years as we have had in the prior two decades ‒ increasing evidence that we are in a new volatility-of-volatility regime. Fundamentally, market impact is an illustration of market inefficiency: theories of efficient markets typically expect that investors buy and sell assets based on assessments of their intrinsic value, in contrast with large derivative players who often act based on market price movements which may not be linked to fundamentals. Market impact risk refers to the degree to which large size transactions can be carried out in a timely fashion with a minimal impact on prices. As a result, managing investment and liquidity risks for large players requires introducing an explicit market impact function, and applying to derivatives significantly depends on whether there is or not significant delta hedging activity: in case of no significant delta hedging activity, the risk appetite has significant influence on the optimal execution strategy, while in case of significant delta hedging activity the optimal trading involves feedback hedging effects translating into a modified Black ‒ Scholes hedging strategy.

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    • Fig. 1. Almost as many transitions from lows to highs over the past 7 years as in the prior 20 years
    • Fig. 2. Sudden drops in SPX realized volatility from high levels to very low levels have become increasingly common
    • Fig. 3. Expiration week return vs. net-delta of front-month S&P options on previous Friday
    • Fig. 4. Gamma as a function of spot S&P 500 index options
    • Fig. 5. Put price as a function of the moneyness
    • Fig. 6. The mean cost optimal strategy under the Black and Scholes model
    • Fig. 7. The rate of trading as a function of the underlying price S and time t for different values of λ : mean objective (λ = 0 top left) or mean-variance (λ=1 top right, 10 bottom left, 100 bottom right)
    • Fig. 8. Sample paths of the evolution of the fundamental price, trading rate, inventory and traded quantity throughout the execution for λ= 100
    • Fig. 9. European call price
    • Fig. 10. European call price gap between B&S and Feedback effect price
    • Fig. 11. The B&S gamma hedging strategy
    • Fig. 12. The B&S delta hedging strategy
    • Table 1. S&P 500 Historical Volume Data (2 Jan. 1951 – 31 Mar. 2012)
    • Table 2. Listed options – most actively traded and open interest – S&P500 index options
    • Table 3. Simulations inputs parameters