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多標的資產衍生性商品之EPMS 價格估計量 = An EPMS Pric...

國立高雄大學統計學研究所

多標的資產衍生性商品之EPMS 價格估計量 = An EPMS Price Estimator for Multi-Asset Financial Derivatives

Record Type:	Language materials, printed : monographic
Paralel Title:	An EPMS Price Estimator for Multi-Asset Financial Derivatives
Author:	邱冠智,
Secondary Intellectual Responsibility:	國立高雄大學
Place of Publication:	[高雄市]
Published:	國立高雄大學;
Year of Publication:	2015[民104]
Description:	[3]，37葉圖，表 : 30公分;
Subject:	P測度下之鞅模擬法
Subject:	Empirical P-martingale simulation
Online resource:	https://hdl.handle.net/11296/gxymd7
Notes:	109年11月18日公開
Summary:	本文考慮多標的資產衍生性商品的EPMS (empirical P-martingale simulation) 價格估計量,並藉由多維度Girsanov定理與Esscher轉換推導風險中立測度變換過程。在收益函數滿足適當的假設下,本文推導出多標的資產衍生性商品EPMS價格估計量的一致性,本文亦對多標的資產衍生性商品的EPMS價格估計量提出一推測之漸近分佈。在模擬研究中,考慮幾何平均賣權與最大報酬買權的定價,並分別在標的資產滿足多維度幾何布朗運動或多維度GARCH模型的假設下,發現多標的資產衍生性商品的EPMS價格估計量不僅準確,且能提升傳統Monte Carlo價格估計量的有效性,數值模擬的結果也支持本文所推測之漸近常態分佈具有良好的近似效果。 This article considers the empirical P-martingale simulation (EPMS) price estimator for multi-asset financial derivatives. The corresponding change of measure process of a stochastic model is derived by the multiple dimensional Girsanov theorem or Esscher transform. Under mild assumptions on the payoff functions, the consistency of the multi-asset EPMS price estimator is established. We also make a conjecture on the asymptotic distribution for the multi-asset EPMS price estimator. In simulation study, geometric average put option and maximum call option pricing are considered under multivariate geometric Brownian motion and GARCH models. Numerical results indicate that the multi-asset EPMS price estimator is accurate and is capable of improving the efficiency of traditional Monte Carlo price estimator. The results also provide strong evidence that the asymptotic distribution approximates the nominal values very well in our scenarios.

多標的資產衍生性商品之EPMS 價格估計量 = An EPMS Price Estimator for Multi-Asset Financial Derivatives
邱, 冠智

多標的資產衍生性商品之EPMS 價格估計量 = An EPMS Price Estimator for Multi-Asset Financial Derivatives / 邱冠智撰 - [高雄市] : 國立高雄大學, 2015[民104]. - [3]，37葉 ; 圖，表 ; 30公分.
109年11月18日公開.
參考書目：葉31-32.
P測度下之鞅模擬法Empirical P-martingale simulation

多標的資產衍生性商品之EPMS 價格估計量 = An EPMS Price Estimator for Multi-Asset Financial Derivatives
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330 $a 本文考慮多標的資產衍生性商品的EPMS (empirical P-martingale simulation) 價格估計量,並藉由多維度Girsanov定理與Esscher轉換推導風險中立測度變換過程。在收益函數滿足適當的假設下,本文推導出多標的資產衍生性商品EPMS價格估計量的一致性,本文亦對多標的資產衍生性商品的EPMS價格估計量提出一推測之漸近分佈。在模擬研究中,考慮幾何平均賣權與最大報酬買權的定價,並分別在標的資產滿足多維度幾何布朗運動或多維度GARCH模型的假設下,發現多標的資產衍生性商品的EPMS價格估計量不僅準確,且能提升傳統Monte Carlo價格估計量的有效性,數值模擬的結果也支持本文所推測之漸近常態分佈具有良好的近似效果。 This article considers the empirical P-martingale simulation (EPMS) price estimator for multi-asset financial derivatives. The corresponding change of measure process of a stochastic model is derived by the multiple dimensional Girsanov theorem or Esscher transform. Under mild assumptions on the payoff functions, the consistency of the multi-asset EPMS price estimator is established. We also make a conjecture on the asymptotic distribution for the multi-asset EPMS price estimator. In simulation study, geometric average put option and maximum call option pricing are considered under multivariate geometric Brownian motion and GARCH models. Numerical results indicate that the multi-asset EPMS price estimator is accurate and is capable of improving the efficiency of traditional Monte Carlo price estimator. The results also provide strong evidence that the asymptotic distribution approximates the nominal values very well in our scenarios.
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