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Stochastic Processes in Complex Financial Economic Systems = = 複雜金融經濟系統中的隨機過程

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Stochastic Processes in Complex Financial Economic Systems =/
其他題名:	複雜金融經濟系統中的隨機過程
作者:	Liu, Chi Hei Christopher.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2021,
面頁冊數:	144 p.
附註:	Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
Contained By:	Dissertations Abstracts International83-05B.
標題:	Statistical physics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28851424
ISBN:	9798492728021

Stochastic Processes in Complex Financial Economic Systems = = 複雜金融經濟系統中的隨機過程
Liu, Chi Hei Christopher.

Stochastic Processes in Complex Financial Economic Systems =複雜金融經濟系統中的隨機過程 - Ann Arbor : ProQuest Dissertations & Theses, 2021 - 144 p.

Source: Dissertations Abstracts International, Volume: 83-05, Section: B.

Thesis (Ph.D.)--The Chinese University of Hong Kong (Hong Kong), 2021.

This thesis contains two different topics under the common umbrella of analysing and solving quantitative finance problems subject to the Cox-Ingersoll-Ross (CIR) process with physics approach. In the first part of the thesis, we focus on option pricing under the Heston stochastic volatility with time-dependent parameters. The Heston model assumes that the price of the underlying is determined by the Black-Scholes type stochastic process while the variance is a time-dependent CIR process. Starting with the special case, where the volatility of the volatility is zero and applying the Wei-Norman theorem, an analytical formula for pricing European vanilla options, with an arbitrary time-dependent long-term variance, is derived in terms of the Black-Scholes formula. Subsequently, we determine the exact error correction function for non-zero volatility of the variance and approximate the error correction function by Lie-Trotter splitting and Taylor expansion, which can be computed numerically and gives accurate results. We also improve the accuracy by reiterating the calculation of the error correction function. In addition, we obtain the approximation for option pricing subjects to one or two barriers by replacing the Black-Scholes solution of vanilla options with barrier options' solution and kernels.In the second part of the thesis, we focus on the fundamental dynamic of the exchange rate. We present an exchange rate model which the spot of exchange rate is confined in either a wide moving band or target zone and a currency crash occurs when the spot of exchange rate breaches the defined boundary. We derived a solution from the standard log exchange rate equation for the model with a smooth-pasting condition at the defined boundary. The probability of leakage for the exchange rate to cross the boundary increases when the mean-reverting force of the exchange rate is weakened, which implies a rise in currency crash risk. Moreover, we have succeeded in performing explicit calibration of the proposed fundamental dynamics, thus confirming the validity of our model. Unlike the Krugman model, our model is capable of explaining the empirical observations that the exchange rate dynamics is sticky near the edges of the band, and that both positive and negative interest rate differentials can appear in the entire target zone. In addition, the model is also able to determine the crash risk of the G10 currencies during the Global Financial Crisis in 2008 and gives evidence that the transitions of the exchange rate between the two regimes cause changes in the level of the exchange rate volatility but not the dynamical structure.

ISBN: 9798492728021Subjects--Topical Terms:

536281
Statistical physics.
Subjects--Index Terms:

Stochastic processes

Stochastic Processes in Complex Financial Economic Systems = = 複雜金融經濟系統中的隨機過程
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300 $a 144 p.
500 $a Source: Dissertations Abstracts International, Volume: 83-05, Section: B.
500 $a Advisor: Ong, Hock Chun Daniel.
502 $a Thesis (Ph.D.)--The Chinese University of Hong Kong (Hong Kong), 2021.
520 $a This thesis contains two different topics under the common umbrella of analysing and solving quantitative finance problems subject to the Cox-Ingersoll-Ross (CIR) process with physics approach. In the first part of the thesis, we focus on option pricing under the Heston stochastic volatility with time-dependent parameters. The Heston model assumes that the price of the underlying is determined by the Black-Scholes type stochastic process while the variance is a time-dependent CIR process. Starting with the special case, where the volatility of the volatility is zero and applying the Wei-Norman theorem, an analytical formula for pricing European vanilla options, with an arbitrary time-dependent long-term variance, is derived in terms of the Black-Scholes formula. Subsequently, we determine the exact error correction function for non-zero volatility of the variance and approximate the error correction function by Lie-Trotter splitting and Taylor expansion, which can be computed numerically and gives accurate results. We also improve the accuracy by reiterating the calculation of the error correction function. In addition, we obtain the approximation for option pricing subjects to one or two barriers by replacing the Black-Scholes solution of vanilla options with barrier options' solution and kernels.In the second part of the thesis, we focus on the fundamental dynamic of the exchange rate. We present an exchange rate model which the spot of exchange rate is confined in either a wide moving band or target zone and a currency crash occurs when the spot of exchange rate breaches the defined boundary. We derived a solution from the standard log exchange rate equation for the model with a smooth-pasting condition at the defined boundary. The probability of leakage for the exchange rate to cross the boundary increases when the mean-reverting force of the exchange rate is weakened, which implies a rise in currency crash risk. Moreover, we have succeeded in performing explicit calibration of the proposed fundamental dynamics, thus confirming the validity of our model. Unlike the Krugman model, our model is capable of explaining the empirical observations that the exchange rate dynamics is sticky near the edges of the band, and that both positive and negative interest rate differentials can appear in the entire target zone. In addition, the model is also able to determine the crash risk of the G10 currencies during the Global Financial Crisis in 2008 and gives evidence that the transitions of the exchange rate between the two regimes cause changes in the level of the exchange rate volatility but not the dynamical structure.
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653 $a Financial economic systems
653 $a Cox-Ingersoll-Ross
653 $a Exchange rate
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690 $a 0508
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710 2 $a The Chinese University of Hong Kong (Hong Kong). $3 1017547
773 0 $t Dissertations Abstracts International $g 83-05B.
790 $a 1307
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793 $a English
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