×
Cohen, Samuel N.; Reisinger, Christoph; Wang, Sheng

Hedging option books using neural-SDE market models. (English) Zbl 1520.91400

Appl. Math. Finance 29, No. 5, 366-401 (2022).
Summary: We study the capability of arbitrage-free neural-SDE market models to yield effective strategies for hedging options. In particular, we derive sensitivity-based and minimum-variance-based hedging strategies using these models and examine their performance when applied to various option portfolios using real-world data. Through backtesting analysis over typical and stressed market periods, we show that neural-SDE market models achieve lower hedging errors than Black-Scholes delta and delta-vega hedging consistently over time, and are less sensitive to the tenor choice of hedging instruments. In addition, hedging using market models leads to similar performance to hedging using Heston models, while the former tends to be more robust during stressed market periods.

Cited in 2 Documents

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60H35 Computational methods for stochastic equations (aspects of stochastic analysis)

Keywords:

market models; European options; market simulators; no-arbitrage; neural-SDE; hedging
Cite Review PDF
Full Text: DOI arXiv

References:

[1] Albrecher, H.; Mayer, P.; Schoutens, W.; Tistaert, J., The Little Heston Trap, Wilmott, 1, 83-92 (2007)
[2] Alexander, C.; Kaeck, A., Does Model Fit Matter for Hedging? Evidence From FTSE 100 Options, Journal of Futures Markets, 32, 7, 609-638 (2012) · doi:10.1002/fut.20537
[3] Alexander, C.; Nogueira, L. M., Model-free Hedge Ratios and Scale-invariant Models, Journal of Banking & Finance, 31, 6, 1839-1861 (2007) · doi:10.1016/j.jbankfin.2006.11.011
[4] Bakshi, G.; Cao, C.; Chen, Z., Empirical Performance of Alternative Option Pricing Models, The Journal of Finance, 52, 5, 2003-2049 (1997) · doi:10.1111/j.1540-6261.1997.tb02749.x
[5] Bates, D. S., Post-’87 Crash Fears in the S&P 500 Futures Option Market, Journal of Econometrics, 94, 1-2, 181-238 (2000) · Zbl 0942.62118 · doi:10.1016/S0304-4076(99)00021-4
[6] Black, F.1976. “Studies of Stock Market Volatility Changes.” In 1976 Proceedings of the American Statistical Association Buisness and Economic Statistics Section, 177-181.
[7] Black, F.; Scholes, M., The Pricing of Options and Corporate Liabilities, Journal of Political Economy, 81, 3, 637-54 (1973) · Zbl 1092.91524 · doi:10.1086/260062
[8] Boyarchenko, S.; LevendorskiÄŋ, S., Static and Semistatic Hedging As Contrarian Or Conformist Bets, Mathematical Finance, 30, 3, 921-960 (2020) · Zbl 1508.91551 · doi:10.1111/mafi.v30.3
[9] Broadie, M.; Chernov, M.; Johannes, M., Model Specification and Risk Premia: Evidence From Futures Options, The Journal of Finance, 62, 3, 1453-1490 (2007) · doi:10.1111/j.1540-6261.2007.01241.x
[10] Buehler, H.; Gonon, L.; Teichmann, J.; Wood, B., Deep Hedging, Quantitative Finance, 19, 8, 1271-1291 (2019) · Zbl 1420.91450 · doi:10.1080/14697688.2019.1571683
[11] Caron, R. J.; McDonald, J. F.; Ponic, C. M., A Degenerate Extreme Point Strategy for the Classification of Linear Constraints As Redundant Or Necessary, Journal of Optimization Theory and Applications, 62, 2, 225-237 (1989) · Zbl 0651.90047 · doi:10.1007/BF00941055
[12] Carr, P., Ellis, K., and Gupta, V.. 1999. “Static Hedging of Exotic Options.” In Quantitative Analysis In Financial Markets: Collected Papers of the New York University Mathematical Finance Seminar, 152-176. World Scientific.
[13] Carr, P.; Geman, H.; Madan, D.; Yor, M., Stochastic Volatility for Lévy Processes, Mathematical Finance, 13, 3, 345-382 (2003) · Zbl 1092.91022 · doi:10.1111/mafi.2003.13.issue-3
[14] Carr, P.; Madan, D. B., A Note on Sufficient Conditions for No Arbitrage, Finance Research Letters, 2, 3, 125-130 (2005) · doi:10.1016/j.frl.2005.04.005
[15] CBOE. 2019. “White Paper: CBOE Volatility Index.” Accessed April 08, 2021. https://cdn.cboe.com/resources/vix/vixwhite.pdf.
[16] Cohen, S. N.; Reisinger, C.; Wang, S., Detecting and Repairing Arbitrage in Traded Option Prices, Applied Mathematical Finance, 27, 5, 345-373 (2020) · Zbl 1466.91331 · doi:10.1080/1350486X.2020.1846573
[17] Cohen, S. N., Reisinger, C., and Wang, S.. 2021. Arbitrage-Free Neural-SDE Market Models. arXiv:2105.11053.
[18] Cohen, S. N.; Reisinger, C.; Wang, S., Estimating Risks of Option Books Using Neural-SDE Market Models, Journal of Computational Finance, 26, 3, 33-72 (2022) · doi:10.21314/JCF.2022.028
[19] Cohen, S. N., Snow, D., and Szpruch, L.. 2021. Black-Box Model Risk in Finance. arXiv:2102.04757.
[20] Cont, R.; Tankov, P., Financial Modelling with Jump Processes (2004), Raton, Florida: Chapman and Hall/CRC · Zbl 1052.91043
[21] Cousot, L., Conditions on Option Prices for Absence of Arbitrage and Exact Calibration, Journal of Banking & Finance, 31, 11, 3377-3397 (2007) · doi:10.1016/j.jbankfin.2007.04.006
[22] Davis, M. H. A.; Hobson, D. G., The Range of Traded Option Prices, Mathematical Finance, 17, 1, 1-14 (2007) · Zbl 1278.91158 · doi:10.1111/mafi.2007.17.issue-1
[23] Föllmer, H., and Schweizer, M.. 1990. “Hedging of Contingent Claims Under Incomplete Information.” In Applied Stochastic Analysis, edited by M. Davis and R. Elliott, 389-414. London: Stochastics Monographs Gordon & Breach. · Zbl 0738.90007
[24] Hagan, P. S.; Kumar, D.; Lesniewski, A. S.; Woodward, D. E., Managing Smile Risk, Wilmott Magazine, 1, 84-108 (2002)
[25] Hagan, P. S.; Kumar, D.; Lesniewski, A. S.; Woodward, D. E., Arbitrage-free SABR, Wilmott, 69, 69, 60-75 (2014) · doi:10.1002/wilm.10290
[26] Hayashi, T.; Mykland, P. A., Evaluating Hedging Errors: An Asymptotic Approach, Mathematical Finance, 15, 2, 309-343 (2005) · Zbl 1153.91505 · doi:10.1111/mafi.2005.15.issue-2
[27] Heston, S. L., A Closed-form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, Review of Financial Studies, 6, 2, 327-343 (1993) · Zbl 1384.35131 · doi:10.1093/rfs/6.2.327
[28] Hull, J.; White, A., Optimal Delta Hedging for Options, Journal of Banking & Finance, 82, 180-190 (2017) · doi:10.1016/j.jbankfin.2017.05.006
[29] Kim, K.-K.; Lim, D.-Y., Static Replication of Barrier-type Options Via Integral Equations, Quantitative Finance, 21, 2, 281-294 (2021) · Zbl 1466.91343 · doi:10.1080/14697688.2020.1817973
[30] Kirkby, J. L.; Deng, S., Static Hedging and Pricing of Exotic Options with Payoff Frames, Mathematical Finance, 29, 2, 612-658 (2019) · Zbl 1411.91567 · doi:10.1111/mafi.2019.29.issue-2
[31] Leung, T.; Ward, B., Dynamic Index Tracking and Risk Exposure Control Using Derivatives, Applied Mathematical Finance, 25, 2, 180-212 (2018) · Zbl 1418.91522 · doi:10.1080/1350486X.2018.1507750
[32] Merton, R. C., Option Pricing when Underlying Stock Returns are Discontinuous, Journal of Financial Economics, 3, 1-2, 125-144 (1976) · Zbl 1131.91344 · doi:10.1016/0304-405X(76)90022-2
[33] OptionMetrics. 2020. “IvyDB Europe Reference Manual.” https://wrds-www.wharton.upenn.edu/documents/1447/IvyDB_Europe_Reference_Manual_wEX3ZW6.pdf. Version 2.4.
[34] Poulsen, R.; Schenk-Hoppé, K. R.; Ewald, C.-O., Risk Minimization in Stochastic Volatility Models: Model Risk and Empirical Performance, Quantitative Finance, 9, 6, 693-704 (2009) · Zbl 1188.91220 · doi:10.1080/14697680902852738
[35] Rebonato, R., Volatility and Correlation: The Perfect Hedger and the Fox (2005), Chichester, Surrey: John Wiley & Sons
[36] Ruf, J.; Wang, W., Neural Networks for Option Pricing and Hedging: A Literature Review, Journal of Computational Finance, 24, 1, 1-46 (2020) · doi:10.21314/JCF.2020.390
[37] Ruf, J.; Wang, W., Hedging with Linear Regressions and Neural Networks, Journal of Business & Economic Statistics, 40, 4, 1442-1454 (2021) · Zbl 07928269 · doi:10.1080/07350015.2021.1931241
[38] Schweizer, M., Option Hedging for Semimartingales, Stochastic Processes and Their Applications, 37, 2, 339-363 (1991) · Zbl 0735.90028 · doi:10.1016/0304-4149(91)90053-F
[39] Tankov, P.2011. “Pricing and Hedging in Exponential Lévy Models: Review of Recent Results.” Paris-Princeton Lectures on Mathematical Finance 2010, 319-359. · Zbl 1205.91161
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.