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归因 FX 期权估值差异：波动率与远期输入

文章 Quant Q&A · 作者: Ronnie
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总结

本文探讨如何解释两个系统在类似布莱克–斯科尔斯的框架下，对同一 AUD/JPY 期权估值产生的盯市差异。两个系统报告的隐含波动率、远期汇率、维加和 USD 德尔塔各不相同。问题在于，估值差距有多少来自波动率和远期汇率输入，剩余部分是否也能解释。

回答没有提供数值归因方法，而是指出几种可能造成剩余差异的因素：伽马和其他高阶敏感度、不同的利率假设，以及交叉货币期权 USD 德尔塔表示惯例不一致。回答建议使用 Garman–Kohlhagen 模型，该模型在布莱克–斯科尔斯基础上纳入两种货币各自的利率。因此，比较系统输出时需要统一利率曲线，并明确维加和德尔塔所采用的货币与对冲惯例；仅凭一阶希腊值估算可能无法解释全部盯市差距。

核心观点

  • 隐含波动率和远期汇率的差异可能造成 FX 期权盯市估值差距。
  • 由于伽马和其他高阶效应，一阶希腊值估算后仍可能存在估值差异。
  • 不同的利率假设可能显著改变交叉货币期权估值。
  • Garman–Kohlhagen 模型纳入了两种货币各自的利率。
  • USD 德尔塔的惯例可能不同，因此应确认各系统中德尔塔的含义。

标签

外汇期权衍生品定价波动率
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# How to break down an FX option P&L?


# How to break down an FX option P&L?












I am comparing the mark-to-market (MtM) valuations of two risk systems, with respect to FX Options.

My question is can I quantify the difference in MtM given the following:

System1

AUD/JPY, MTM = USD 461,000, Implied Vol. = 11.88%, Vega = USD 82,000, Forward Rate = 97.29 and USD Delta = -15,300,000

System2

AUD/JPY, MTM = USD 406,000, Implied Vol. = 12.14%, Vega = USD 77,000, Forward Rate = 97.81 and USD Delta = -13,600,000

Assuming both systems use Black Scholes, how can I quantify the difference in MtM (in USD) which is USD 55,000 by attributing it to:

- Difference in Implied Volatility and;

- Difference in Forward Rates?

I tried doing this and am still left with a small difference - is it possible to quantify that too?

## Answer by q.t.f. (score 1)

https://quant.stackexchange.com/a/16632

Some residual difference is expected due to gamma and other higher order greeks, and to rate assumptions as mentioned above. Also you should make sure about the meaning of delta expressed in USD for an AUD/JPY option; I am not sure that is standard across systems. It could be the dollar value of the JPY to hold as hedge taking AUD as the riskless currency, or dollar value of AUD to hold as hedge taking JPY as riskless currency, or either the value of AUD or JPY to hold for a combined hedge of both currencies' moves against USD. It could also be premium-included or forward versions of these.

## Answer by weismat (score 0)

https://quant.stackexchange.com/a/16614

Did you check that you use the same interest rate for AUD and JPY in both systems? The difference is quite large. The used model should be Garman–Kohlhagen which is Black Scholes with two interest rates. In which currency is the vega?

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