交易信用投資策略之隨機模型

傳統資金管理的成效有賴於對未來現金流量預測之準確性，然而在金融風暴蔓延與貨幣戰爭激烈的不確定年代，產品價格、利率與匯率等風險深深影響公司獲利的穩定性。基於傳統財務管理理論未能充分將企業經營的不確定性納入考量，本論文將價格與利率的不確定性整合至公司理財與投資決策模型中，提出一個在延遲付款下的公司價值評價模型，並進而推導出公司價值的封閉解。接著將公司價值的動態，以隨機動態規劃法與蒙地卡羅模擬法，分別推導出在風險環境下具有延遲支付貨款權益的公司之實質選擇權價值。本論文整合Merton在1973年所發表的隨機利率模型與常見於金融衍生性商品評價的幾何布朗運動隨機價格模型，將其應用在具有交易信用的公司評價與實質選擇權評價模型之建立。在模型的建構過程中，本論文考慮以下諸參數：隨機價格與隨機利率的漂移項與波動性、銷貨成本率、需求的價格彈性、產品的市場占有率、信用期間的長短等。以上諸因素對公司價值與實質選擇權價值的影響程度不一，依其重要性排序，可提供經營管理者投資決策與風險控管之依據。在本文中，風險性與隨機性的源頭來自於價格與利率的動態過程，這與日常管理實務上的經驗不謀而合，而公司營運活動的營收與盈餘受到這兩股具有高度不確定性的因子影響，未來現金流量亦呈現隨機波動之現象，乃至於公司價值亦是一個隨機漂移的過程。本文將管理實務上常見的交易信用制度整合至隨機模型中，使得模型本身更具備有管理上的意涵與貢獻。

關鍵字

隨機價格；隨機利率；交易信用；實質選擇權

並列摘要

In the world surrounded by uncertainties ranging from financial crisis to currency war, the volatility of commodity price, interest rate and foreign exchange rate significantly affects the stability of corporate earnings. However, many frameworks of corporate valuation did not explicitly take into account risk factors, which the thesis intends to incorporate in a valuation model for a firm with trade credit under price and interest rate uncertainties. Analytical solutions for corporate value under uncertainties are derived and used as the basis of further formulation for the real option value, representing the investment profits for such a firm with trade credit under uncertainties. The stochastic dynamic programming and Monte Carlo simulation approaches are employed to derive the real option value. This thesis integrates the stochastic interest rate model of Merton (1973) and the geometric Brownian motion model of price into a framework for corporate valuation when a firm facing both the price and the interest rate risks. The risks are propagated from the price, the interest rate, the future cash flows to the corporate value. The supplier allows the firm to defer its merchandise payments due to the trade credit terms. To obtain more earnings, the firm has an opportunity to invest the deferred payment amounts in interest-bearing financial instruments. Other factors considered in this framework include the cost rate, the market share, the price elasticity of demand, and the time length of credit period. The analytical solution for corporate value is derived. Subsequently, the analytical and numerical solutions for the investment threshold and the real option value are obtained. The sensitivity analyses of the corporate value, the investment threshold, and the real option value are performed in illustrations. The managerial implications provide an insight into the investment strategy for the firm under uncertainties.

並列關鍵字

Stochastic Price ； Stochastic Interest Rate ； Trade Credit ； Real Option

參考文獻

[1] Aggarwal, S.P. and Jaggi, C.K. (1995). Ordering policies of deteriorating items under permis-sible delay in payments. The Journal of the Operational Research Society, 46 (5), 658-662.

[3] Black, F. and Cox, J.C. (1976). Valuing corporate securities: Some effects of bond indenture provisions. The Journal of Finance, 31 (2), 351-367.

[4] Black, F. and Karasinski, P. (1991). Bond and option pricing when short rates are lognormal. Financial Analysts Journal, 47 (4), 52-59.

[5] Black, F. and Scholes, M. (1973). The pricing of options and liabilities. The Journal of Politi-cal Economy, 81 (3), 637-654.

[6] Bougheas, S., Mateut, S. and Mizen, P. (2009). Corporate trade credit and inventories: new evidence of a trade-off from accounts payable and receivable. Journal of Banking and Finance, 33 (2), 300-307.

國際替代計量

交易信用投資策略之隨機模型

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