Two Risk Management Problems in Financial Market

金融市場中的兩個風險管理問題

Student thesis: Doctoral Thesis

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Award date2 Aug 2018

Abstract

Risk is one of the commonly mentioned keywords in the financial market. From the potential loss risk of investors that hold portfolios to systemic risk of the whole market, regulators and participants in this financial market all agree on the importance of financial risk management in order to maintain the stability of the market. There are various kinds of risks that one participant may face, such as market risk, liquidity risk, and credit risk, which may be induced by the uncertainty of the market, inappropriate investment etc. And we usually call these quantified potential losses the risk exposure.

Risk management of a financial institutions or investors tries to identify the sources of risk exposure and hedges it via financial instruments. For regulators or governments, financial risk management identifies the sources of large-scale risk that may collapse the infrastructure of the whole financial market.

This thesis solves two important risk management problems in the viewpoint of financial engineering. It investigates the risk management of one financial instrument, portfolio, and the financial market.

The first one focuses on the sensitivity analysis of financial derivatives with multi-underlying assets. A financial institution that sells derivatives to clients in the financial markets is faced with the problem of managing its risk exposure. It is straightforwardly related to sensitivity analysis of derivative price, i.e., greek letters of derivatives because we can invest other
financial instruments that make the overall portfolio greeks neutral in order to hedge the potential loss generated by fluctuation of price. Although Monte Carlo simulation-based stochastic gradient methods, such as finite difference approximation, IPA, and SPA, etc., provide the useful tools so that we can achieve any precision, managers still prefer table look-at methods which are fast but unsafe, because managers urge for the greeks surface information that summarizes all the possible scenarios and stochastic gradient can only consider one scenario once and large computational effort is always required. This issue may become more severe if we consider the derivatives with multiple underlying assets, which makes the corresponding first order and second order greeks a vector and a matrix. In the first part of this thesis, we propose a series of methods that guarantee both the good estimation precision and low computational effort to fit gamma matrix surface of derivatives with multiple underlying assets. Meanwhile, we suggest one useful solution if gamma matrix is of certain property, i.e., positive definiteness. And these proposed methods can be well applied to other problems related to matrix surface fitting. Numerical results show that we have the good performance of gamma surface fitting with the lower computational effort by the proposed methods.

Then, the systemic risk and financial contagion phenomenon of the financial market is considered. As a special financial institution designed for controlling the systemic risk of the financial market, central counterparty clearing house (CCP) is organized in order to prevent financial contagion from breaking linkages among financial institutions and is recommended
by several regulators. This centralized trading structure sometimes relieves the systemic risk of market, but CCP centralizes all the credit risk so that the failure of CCP may result in some severe consequences. So the risk management of CCP is of certain concern in the industry and academy. In the second part of this thesis, we build up a model that captures the trading
structure of participants, i.e., clearing members (CMs), in the CCP as well as the their inner-relationship. And we discuss the estimators of credit risk measurement of CCP. Due to the discontinuity of those estimators, the sensitivity analysis of risk measurements cannot be obtained directly. Here, we find out a method to overcome this difficulty and obtain the gradient estimators of the risk measures. Numerical examples show good performance of proposed estimators. Finally, one straightforward way to manage CCP’s risk is to adjust the margin requirement. We introduce mixed scheme that can both control systemic risk and idiosyncratic risk.

    Research areas

  • Financial risk management, sensitivity analysis, financial derivatives with multi-underlying assets, central counterparty clearing house