跨通貨股酬交換及交換選擇權之評價

傳統對股酬交換的風險中立評價與同期間遠期利率交換評價是一致的，故其定價模式類似於利率交換模型，但在跨通貨的股酬交換則未必如此，國外股價和匯率的價格過程，以及國外資產與匯率的相關係數對交換價值有所影響。本文延伸Chance與Rich(1998)的股酬交換模式，並沿用Amin(1991)、Amin和Bodurtha(1995)、Lin(1997)的間斷時期資產價格設定，利用機率測度轉換的步驟來推導股酬交換的風險中立評價模式，主要觀點在對國外股價指數的無套利報酬預期，除了等於期間國外遠期利率外，必須加上一修正項，以反應期間匯率風險。文中同時對股酬交換的相關衍生產品，如股酬交換選擇權、交換上下限、變動名目本金，以及混合股酬交換的評價模式予以推導。最後由數值模擬可得國外遠期利率波動為決定交換利率的主要因素，而如果匯率與國外股價指數及匯率與遠期利率的波動呈負相關，亦會提高交換利率。

關鍵字

跨通貨股酬交換；股酬交換選擇權；機率測度；風險中立評價

並列摘要

The valuation of equity swap under the condition of risk neutral is similar to the forward interest rate swap with the same period. Therefore, its valuation formula is consistent to interest rate swap model in the traditional methods. But it is not the same as in pricing the cross-currency equity swap. The dymanic prices of foreign stock index and exchange rate, and the correlation coefficients between exchange rates and foreign assets also affect the swap rate. In this paper, we extend Chance and Rich(1998)'s valuation formula of equity swaps, and apply Amin (1991)、Amin and Bodurtha(1995)、Lin(l997)'s dymanic prices of assets in discrete time period. To derive the risk neutral valuation formula of equity swap, it uses the method of transfer probability measure. This study finds the expected return of foreign stock index in the no arbitrage condition, in addition equal to foreign forward interest rate with the same period, must be add a correction term to reflect the exchange rate risk. This paper also derives the pricing formula of equity swaptions、caps、floors、variable notional principal and blended equity swap. Finally, we find the volatility of foreign forward interest rate is the most important factor of pricing the swap rate from numerical simulation. And if the correlation of the volatility of exchange rate and foreign stock index、the correlation of the volatility of exchange rate and foreign forward interest rate are negative, the swap rate will be higher.

並列關鍵字

Cross-currency equity swap ； equity swaption ； probability measure ； risk-neutral valuation formula

參考文獻

Amin, K. I.(1991).On the Computation of Continuous Time Option Prices Using Discrete Approximations.Journal of Financial and Quantitative Analysis.26(4)