Pricing a risk management contract based on a machine learning approach
کد مقاله : 1062-FEMATH5 (R2)
نویسندگان:
مصطفی پورعلی زاده *1، عبدالرحیم بادامچی زاده2، هیربد آسا3
1تهران، خیابان شهید بهشتی، دانشکده علوم ریاضی و رایانه
2عضو هیت علمی/ دانشگاه علامه طباطبائی
3عضو هیت علمی/دانشگاه لیورپول
چکیده مقاله:
The main goal of this paper is to price a risk management‎
problem based on the price of European call options. First‎
of all, we provide a risk management problem which plays‎
the role of an insurance contract to manage the risk of‎
losses caused by market price fluctuation. Then,‎
working towards controlling price movements, we introduce‎
a machine learning algorithm with a quadratic hypothesis‎
to model implied volatility ‎and rule out static arbitrage‎
on call option surface. ‎We ‎address‎ ‎how ‎to ‎preclude ‎over-‎fitting ‎
(high variance) ‎and ‎under-fitting ‎(high bias)‎ ‎‎by a regularized‎
cost function including a penalty‎‎ term which controls the‎
‎trade-off between over-fitting and ‎under-fitting. ‎‎Eventually,‎
‎the results of a numerical ‎implementation‎ show that the‎
proposed modeling‎ of implied volatility yield a‎ volatility‎
surface free‎ of static ‎arbitrage, therefore it can be used to ‎‎
monitor price variability and also to ‎improve the precision‎
‎of contract pricing.‎
کلیدواژه ها:
Risk Management; Implied Volatility; Static Arbitrage; Machine Learning.
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