定价函数要多准

常见的交易侧期望是达到“一个基点量级”的数值精度，例如价格相对误差或绝对误差约 $\boxed{10^{-4}}$。

更合理的回答是：精度应与输入不确定性匹配（尤其 vol、相关、股息等）；如果模型误差远小于 1 vega 对应的价格变化，就通常够用。深 ITM 期权主要是内在价值，真正需要精确的是时间价值部分。

---

英文解析

There are many ways to answer this question. The answer the interviewer was looking for was $1E - 4$ , that is one basis point. Another approach is to consider the uncertainty in the inputs. For example, volatility is estimated rather than observed so an error that is small compared to one Vega is sufficient.

One could also mention that it is error as a fraction of the uncertain part of the price that is important, not as a fraction of the total price. For example, a deeply- in- the- money option is almost all intrinsic, it is the estimate of the value of the optionality that matters.

Here are some possible related questions

• How much is the vega on a one-year at-the-money call option if the stock price is 100?- If your were model were inaccurate, how would you spot the fact?