馬可夫調控共同跳躍擴散過程下跨貨幣選擇權之評價及馬可夫調控CIR經濟下海外可轉債評價之實證分析

Abstract

延伸古典的跳躍擴散模型對於外國股票價格與匯率的動態過程設定，同時考量共同跳躍與時間異質性，建構出馬可夫調控共同跳躍擴散過程並針對外國股票價格、匯率與利率三因子間隨經濟狀態改變而造成的相依程度的變化，與外國股票價格和匯率的各別跳躍與共同跳躍情況對於各種外國股票選擇權和企業赴海外籌資所發行的海外可轉債的影響進行研究。模型參數全都由一個代表經濟隱藏狀態之連續時間且狀態有限的馬可夫鏈所調控。在這樣一個不完全市場設定下，我們運用動態的Esscher轉換來決定一個等價平賭機率測度，並根據推導出的風險中立標的資產價格動態過程來評價各種外國\n股票選擇權與海外可轉債，並提供相關數值分析結果。

We investigate the impact of the change of the dependence among foreign stock prices, exchange rates and interest rates resulted from the regime-switching context of an economy and the idiosyncratic jump and co-jump phenomena between the foreign stock price and the exchange rate on a variety of European-style cross-currency options and European convertible bonds by extending the classical jumpdiffusion model applied to model the dynamics of the foreign stock price and the exchange rate by incorporating the co-jump phenomenon and time-inhomogeneity, then construct the Markov-modulated co-jump-diffusion processes with both idiosyncratic jumps and simultaneous jumps to model the foreign stock price and exchange rate processes.In addition, we consider the interest rate dynamic behavior with regime-switching phenomena, and provide a Markovmodulated CIR process-based framework in interest rate modeling for pricing European convertible bonds. Under an incomplete market setting, we apply the dynamic Esscher transform approach to determine a pricing kernel. According to the resulting dynamics, we provide some numerical analyses.