利用結構式模型評價巨災權益賣權

Abstract

巨災權益賣權(Catastrophe Equity Put 亦稱為CatEPut)，是保險公司在面臨巨災發生時沒有足夠的金額來因應損失而出現的避險商品，保險公司可經由支付賣權之權利金向市場投資者購買此賣權，約定當公司所承保之巨災出險金額超過損失門檻且該公司之股價低於履約價時，公司得行使賣權，並將發行之新股賣給投資人，進而利用獲得的資金作為災後融通之用；另一方面相較於提供再保險契約，購買巨災權益賣權並不會增加再保險公司資產負債表上的負債，有利於信用評等機構給再保險公司較佳的評等。過去的研究如Cox(2004)的巨災選擇權評價模型都直接模擬巨災發生時對股價的影響，而實務上保險出險賠償會直接反映在公司資產價值的減損，公司價值和股價變動複雜的非線性關係無法直接使用改變股價的隨機過程來正確表達。此外，當巨災頻繁發生時保險公司會因為頻繁出險而違約，但Cox(2004)的股價過程只能描述股價滑落，而無法模擬保險公司違約的可能性。本論文假定公司資產服從對數常態分配，巨災頻率使用普瓦松分配，損失則用Zeta distribution模擬對公司資產價值的影響，利用Bino-Trinomial tree實做公司價格隨機過程的變動。並使用結構式模型(Structural model)及複合選擇權(Compound option)的概念處理股價的變動，並分別用三種不同角度評價巨災權益賣權，分別是賣權發行者，保險公司股東以及債權人。

Catastrophe equity puts (“CatEPut”) is a hedging derivative purchased by an insurance company to raising fund for compensating the loss caused by catastrophes. Insurance company pays the premium to investors to buy the option that allows it to sell its own stock at a predetermined strike price to investors in case the loss of ca-tastrophes exceeds a specific threshold and the stock price is lower than the strike price. This capital injection can finance the payments of financial claims and im-prove the financial status of the issuance company. Compared to the reinsurance contract, purchasing catastrophe equity put options does not increase the amounts of liabilities on the balance sheet of reinsurance companies which is advantageous for its credit rating. Past research like Cox (2004) evaluating CatEPut by directly de-scribing the influences of disaster on the stock price. In practice, the insurance com-pany’s compensation directly reduces the company's asset value instead The complex, nonlinear relation between the change of the stock price and the asset value due to occurrences of catastrophes is hard to be directly modeled on the stock price process. Even doing so, the model parameters are hard to be calibrated empirically. In addi-tion, past researches can only naively model the drop of the stock price due to occur-rences of catastrophes but fail to model the default of insurance company due to ina-bility to repay catastrophes’ compensations In this thesis, we assume that the firm value follows lognormal distribution、the intensity of catastrophe follows the Poisson process、 and the magnitude of loss following Zeta distribution. Then we use the Bin-Trinomial tree to model the dynamics of the asset value and use the compound option and structural model to describe the change of stock price and evaluate CatE-Put from three different viewpoints: issuer, equity holder and debt holder.