本文旨在掌握股酬交換市場機制的實際面，發展一個二因子，非馬可夫決策樹來訂定股酬交換之價格。本文延伸Amin and Bodurtha（1995）及Amin（1991）兩文之模型，建立一個容易計算單一貨幣，浮動式股酬交換價格之公式。主要貢獻有兩點：（1）股酬交換之市價提供股價波動性另一引申估計法，（2）股酬交換之價格主要隨股價波動性而變，與利率之波動性、利率高低關係不大。求解電腦程式主要之挑戰不是跑電腦之時間，而是C語言中之動態記憶分配之技巧的運用。因為我們不是用模擬，而是用決策樹求近似解。用電腦IBM RS/6000跑程式一次僅耗時數秒。我們也比較固定及隨機馬氏平賭機率下之股酬交換價格。結果顯示兩者都很接近波動性平方之二分之一。
A two-factor, non-Markovian tree is developed to capture the institutional realities of the equity swap market. Extending Amin and Bodurtha (1995) and Amin (1991), we construct a computable expression for the price (fixed spread, FS) of a single-currency floating equity swap. We find: (1) the market price of the equity swap provides an independent measure for the implied volatility of stock index returns; (2) the fixed spread depends critically on the stock index price volatility but is nearly independent of both the level and the volatility of the interest rates. The critical implementation challenge is not in computation time but rather in dynamic memory allocation programming since we use the tree approach instead of Monte Carlo simulation. For a quarterly settled swap with three-year tenor, it takes just a few seconds of processing time on an IBM RS/6000. We compare equity swap prices under both fixed equiprobable and random datedependent martingale measures. The resulting prices are extremely close and approximately one-half the variance of stock index returns.
