CDS和Monte Carlo simulation的几个问题

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大家好，我现在在美国留学，在准备考CFA。刚注册这个论坛，希望能向大家学习。以下是我遇到的几个问题，还请不吝赐教。

PS: 我的qq是1214877519，有兴趣讨论的同学我们也可以用qq联系。

1. 请问single-name CDS的payoff为什么是“based on the market value of the cheapest-to-deliverbond that has the same seniority as the reference obligation”？为什么不是具有相同seniority的所有bonds的market values的平均值？

2．Study Notes在讲完CDS spread的计算方法之后，马上又说了一句：“We can also quote the CDS price as: price of CDS (per$100 notional) = $100 - upfront premium。”

在我的印象当中，我一直以为在买卖CDS的当时，买卖双方只支付upfront premium（如果这是个正数，则买方付给卖方；如果是负数，则卖方付给买方）；而在买卖完成之后，则是买方给卖方支付CDS coupon。所以我不理解为什么还需要引入这个“CDS price”的概念？这个“CDS price”是哪一方付给哪一方的？是在买卖CDS的当时还是买卖之后支付的？

3. Supposethat the process followed by the underlying stock price in a risk-neutral worldis

dS =u*S*dt + sigma*S*dz,

wheredz is a Wiener process, u is the expected return in a risk-neutral world, and sigmais the volatility. To simulate the path followedby S, we can divide the life of the derivative into N short intervals of lengthDelta_t and approximate the above equation as

S(t +Delta_t) - S (t) = u*S(t)*Delta_t + sigma*S(t)*epsilon*SquareRoot(Delta_t),

whereepsilon is a random sample from a standard normal distribution.

我想确认一下：这里之所以用根号Delta_t，是为了保证sigma*S(t)*epsilon*SquareRoot(Delta_t)的方差约等于sigma*S*dz的方差，对吗？

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关键词：Monte Carlo Simulation ulation Carlo ATION reference 美国留学 计算方法 market values

1 Under most efficient market,we use the cheapest one,other than the average of the similar ones, to calculate the payoff. (easier for calculation, for volatility, for other pricing purpose,etc). The 'average' is applicable for other exotic products such as lookback or asia options.
2.CDS pricing is used as input for other interest calibrated models. That's why we need it. It's not necessary for direct trading.
3 Your understanding is not statistically correct. But it's fine. Just remember the formula.