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跳躍擴散模型下之短期利率期貨與結構型債券評價邵智羚 Unknown Date (has links)
經由愈來愈多的實證研究發現,的確在利率的變動過程中,除了包含連續性行為,即遵循”擴散”模式(diffusion process),亦包含了不連續性行為,也就是有著跳躍(jump)的情形發生。因此顯示出假設利率隨機過程僅為連續性的擴散模型已是不足夠的,跳躍-擴散模型(Jump-diffusion model)顯然會比純粹擴散模型有著更好的解釋能力。而市場模型(LIBOR market model)的提出,則說明了遠期LIBOR利率模型較能描述市場實際的利率型態,並且可方便使用市場資訊,進行模型參數校準。
所以本研究旨在以LIBOR market model 加上跳躍過程,即遠期LIBOR利率的跳躍-擴散模型,分別針對歐洲美元期貨與利率結構型債券中的滾雪球式累息債券建立評價方法。由於所選用動態模型的複雜度,使得封閉解的求出不易,因此在文中,最後是採用蒙地卡羅模擬法,求兩商品的數值解。在後續研究上,本文還挑出了幾個最直接影響商品價值的因素,如殖利率、波動度、跳躍幅度等,進行各種情境下商品價值的敏感度分析,以提供投資人與發行商在考量風險因子所在時的一個參考。
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Empirical Performance and Asset Pricing in Markov Jump Diffusion Models / 馬可夫跳躍擴散模型的實證與資產定價林士貴, Lin, Shih-Kuei Unknown Date (has links)
為了改進Black-Scholes模式的實證現象,許多其他的模型被建議有leptokurtic特性以及波動度聚集的現象。然而對於其他的模型分析的處理依然是一個問題。在本論文中,我們建議使用馬可夫跳躍擴散過程,不僅能整合leptokurtic與波動度微笑特性,而且能產生波動度聚集的與長記憶的現象。然後,我們應用Lucas的一般均衡架構計算選擇權價格,提供均衡下當跳躍的大小服從一些特別的分配時則選擇權價格的解析解。特別地,考慮當跳躍的大小服從兩個情況,破產與lognormal分配。當馬可夫跳躍擴散模型的馬可夫鏈有兩個狀態時,稱為轉換跳躍擴散模型,當跳躍的大小服從lognormal分配我們得到選擇權公式。使用轉換跳躍擴散模型選擇權公式,我們給定一些參數下研究公式的數值極限分析以及敏感度分析。 / To improve the empirical performance of the Black-Scholes model, many alternative models have been proposed to address the leptokurtic feature of the asset return distribution, and the effects of volatility clustering phenomenon. However,
analytical tractability remains a problem for most of the alternative models. In this dissertation, we propose a Markov jump diffusion model, that can not only incorporate both the leptokurtic feature and volatility smile, but also present the economic features of volatility clustering and long memory.
Next, we apply Lucas's general equilibrium framework to evaluate option price, and to provide analytical solutions of the equilibrium price for European call options when the jump size follows some specific distributions. In particular, two cases are considered, the defaultable one and the lognormal distribution. When the underlying Markov chain of the Markov jump diffusion model has two states, the so-called switch jump diffusion model, we write an explicit analytic formula under the jump size has a lognormal distribution. Numerical approximations of the option prices as well as sensitivity analysis are also given.
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確定提撥制退休金之評價:馬可夫調控跳躍過程模型下股價指數之實證 / Valuation of a defined contribution pension plan: evidence from stock indices under Markov-Modulated jump diffusion model張玉華, Chang, Yu Hua Unknown Date (has links)
退休金是退休人未來生活的依靠,確保在退休後能得到適足的退休給付,政府在退休金上實施保證收益制度,此制度為最低保證利率與投資報酬率連結。本文探討退休金給付標準為確定提撥制,當退休金的投資報酬率是根據其連結之股價指數的表現來計算時,股價指數報酬率的模型假設為馬可夫調控跳躍過程模型,考慮市場狀態與布朗運動項、跳躍項的跳躍頻率相關,即為Elliot et al. (2007) 的模型特例。使用1999年至2012年的道瓊工業指數與S&P 500指數的股價指數對數報酬率作為研究資料,採用EM演算法估計參數及SEM演算法估計參數共變異數矩陣。透過概似比檢定說明馬可夫調控跳躍過程模型比狀態轉換模型、跳躍風險下狀態轉換模型更適合描述股價指數報酬率變動情形,也驗證馬可夫調控跳躍過程模型具有描述報酬率不對稱、高狹峰及波動叢聚的特性。最後,假設最低保證利率為固定下,利用Esscher轉換法計算不同模型下型I保證之確定提撥制退休金的評價公式,從公式中可看出受雇人提領的退休金價值可分為政府補助與個人帳戶擁有之退休金兩部分。以執行敏感度分析探討估計參數對於馬可夫調控跳躍過程模型評價公式的影響,而型II保證之確定提撥制退休金的價值則以蒙地卡羅法模擬並探討其敏感度分析結果。 / Pension plan make people a guarantee life in their retirement. In order to ensure the appropriate amount of pension plan, government guarantees associated with pension plan which ties minimum rate of return guarantees and underlying asset rate of return. In this paper, we discussed the pension plan with defined contribution (DC). When the return of asset is based on the stock indices, the return model was set on the assumption that markov-modulated jump diffusion model (MMJDM) could the Brownian motion term and jump rate be both related to market states. This model is the specific case of Elliot et al. (2007) offering. The sample observations is Dow-Jones industrial average and S&P 500 index from 1999 to 2012 by logarithm return of the stock indices. We estimated the parameters by the Expectation-Maximization (EM) algorithm and calculated the covariance matrix of the estimates by supplemented EM (SEM) algorithm. Through the likelihood ratio test (LRT), the data fitted the MMJDM better than other models. The empirical evidence indicated that the MMJDM could describe the asset return for asymmetric, leptokurtic, volatility clustering particularly. Finally, we derived different model's valuation formula for DC pension plan with type-I guarantee by Esscher transformation under rate of return guarantees is constant. From the formula, the value of the pension plan could divide into two segment: government supplement and employees deposit made pension to their personal bank account. And then, we done sensitivity analysis through the MMJDM valuation formula. We used Monte Carlo simulations to evaluate the valuation of DC pension plan with type-II guarantee and discussed it from sensitivity analysis.
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可轉債評價 --- LSMC考慮股價跳躍及信用風險 / Convertible Bond Pricing --- Consider Jump-diffusion model and credit risk with LSMC丁柏嵩 Unknown Date (has links)
可轉換公司債是一種在持有期間內,投資人可以在規定的時間內將債券轉換為股票,或是到期時得到債券報酬的一種複合式證券。因此,可轉債除了具有債券性質之外,還包含另一部份可視為一美式選擇權的股票選擇權。
本篇論文將可轉換債券評價結合數值分析中的最小蒙地卡羅法(Least square monte carlo),使得在評價可轉債時,能夠具有更多的彈性處理發行公司自行設計的贖回條款與其他各種不同的契約情況。
此外,本篇論文針對股價考慮跳躍的性質,使用Compound Poisson 過程模擬發生跳躍的次數,導入Merton的跳躍模型(Jump-diffusion Model),在Merton的假設下,模擬未來股價的動態變化。
信用風險方面,本文採用Duffie提出的風險CIR模型評價。考慮存活函數(Survival Function)和違約強度(Hazard Rate Function),使用CIR模型描述信用違約強度在可轉債持有期間的動態變化,最後模擬出違約的時點,結合LSMC下的可轉債評價評價法。
最後利率部份,雖然Brennan and Schwartz(1980)認為隨機利率對於可轉換債券的評價,並沒有明顯的效果,反而會降低評價時的效率,但是為了符合評價過程的合理性,本文使用CIR短期利率模型。
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Efficient Monte Carlo Simulation for Counterparty Credit Risk Modeling / Effektiv Monte Carlo-simulering för modellering av motpartskreditriskJohansson, Sam January 2019 (has links)
In this paper, Monte Carlo simulation for CCR (Counterparty Credit Risk) modeling is investigated. A jump-diffusion model, Bates' model, is used to describe the price process of an asset, and the counterparty default probability is described by a stochastic intensity model with constant intensity. In combination with Monte Carlo simulation, the variance reduction technique importance sampling is used in an attempt to make the simulations more efficient. Importance sampling is used for simulation of both the asset price and, for CVA (Credit Valuation Adjustment) estimation, the default time. CVA is simulated for both European and Bermudan options. It is shown that a significant variance reduction can be achieved by utilizing importance sampling for asset price simulations. It is also shown that a significant variance reduction for CVA simulation can be achieved for counterparties with small default probabilities by employing importance sampling for the default times. This holds for both European and Bermudan options. Furthermore, the regression based method least squares Monte Carlo is used to estimate the price of a Bermudan option, resulting in CVA estimates that lie within an interval of feasible values. Finally, some topics of further research are suggested. / I denna rapport undersöks Monte Carlo-simuleringar för motpartskreditrisk. En jump-diffusion-modell, Bates modell, används för att beskriva prisprocessen hos en tillgång, och sannolikheten att motparten drabbas av insolvens beskrivs av en stokastisk intensitetsmodell med konstant intensitet. Tillsammans med Monte Carlo-simuleringar används variansreduktionstekinken importance sampling i ett försök att effektivisera simuleringarna. Importance sampling används för simulering av både tillgångens pris och, för estimering av CVA (Credit Valuation Adjustment), tidpunkten för insolvens. CVA simuleras för både europeiska optioner och Bermuda-optioner. Det visas att en signifikant variansreduktion kan uppnås genom att använda importance sampling för simuleringen av tillgångens pris. Det visas även att en signifikant variansreduktion för CVA-simulering kan uppnås för motparter med små sannolikheter att drabbas av insolvens genom att använda importance sampling för simulering av tidpunkter för insolvens. Detta gäller både europeiska optioner och Bermuda-optioner. Vidare, används regressionsmetoden least squares Monte Carlo för att estimera priset av en Bermuda-option, vilket resulterar i CVA-estimat som ligger inom ett intervall av rimliga värden. Slutligen föreslås några ämnen för ytterligare forskning.
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