期權(quán)定價(jià)與動(dòng)態(tài)套利均衡分析-資料下載頁
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【正文】 rCEPV1 1Riskfree rate used as discount rates without risk premium Question: Does riskneutral probability exist and is it unique? Mean or mathematical expectation with riskneutral probability in the imaginary world 30 Fundamental Theorems of Financial Economics The First Financial Economics Theorem: Riskneutral probabilities exist if and only if there are no riskless arbitrage opportunities. The Second Financial Economics Theorem: The riskneutral probabilities are unique if and only if the market is plete. The Third Financial Economics Theorem: Under certain conditions, the ability to revise the portfolio of available securities over time can dynamically make up for the missing securities and effectively plete the market. 31 — Problem and Inverse Problem ? many investors make portfolio changes ? each portfolio’s change is limited ? the aggregation creates a large volume of buying and selling to restore equilibrium ? implying arbitrage opportunity exists ? each arbitrageur wants to take as large position as possible ? a few arbitrageurs bring the price pressures to restore equilibrium Inverse Problem: Knowing the market prices of securities, determine the market’s riskneutral probabilities. Problem: Knowing the market’s riskneutral probabilities, determine the market prices of securities. Unfortunately, are actual securities markets like this ? Are they inplete ? So it would seem that we will not be able to solve the inverse problem。 that is, although riskneutral probabilities may exist, they are not unique. However, in 1954, economist Kenh Arrow saved the day by stating the third fundamental theorem of financial economics, the critical idea behind modern securities pricing theory. 32 — Equivalent Martingale ? Definition: ? ? ? ?? ?? ? ifon l y a n d if ,0 。 , a r bi t r a r ya n y f or , i e spr ob a bi l i t lc on d i t i on a c e r t a i n w i t h pr oc e s s s t oc h a s t i c A , t u r ei n f r a s t r u c ni n f or m a t i o t h e w i t h a n y t i m eA t pr oc e s s . s t oc h a s t i cdr i f t z e r oa is M a r t i n g a l etstsPtS??????????? ?? ? ? ?E S t S ss? ??? ? .m a r t in g a lea is tSThe riskneutral valuation approach is sometimes referred to as using equivalent martingale measure, ., the riskneutral probability is referred to an equivalent martingale measure (probability distribution). 33 Summary of Chapter Five 1. NoArbitrage ? The Key of Finance Theory, Especially For Derivatives Such as Options. 2. Dynamic NoArbitrage Pricing ? RiskNeutral Pricing. 3. Does RiskNeutral Probability Exist and Is It Unique? 4. The Core of Finance Theory — The Fundamental Theorems of Financial Economics
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