Skip to content
All library documents

Closed-Form Pricing for Floating-Strike Geometric Asian Options

Article Quant Q&A · Author: nachofest
Read the original

Summary

The document gives risk-neutral valuation formulas for continuously monitored geometric-average Asian options with a floating strike. It uses a symmetry between a floating-strike call and a fixed-strike put: after substituting the relevant parameters into the fixed-put formula, it presents expressions for both the call and put in terms of the current asset price, maturity, rate, volatility, and normal distribution probabilities.

The formulas assume a stock with no dividends and specify the associated d-values using maturity and volatility. The note points to published option-pricing references but provides no derivation, numerical example, or validation. Its scope is limited to the stated continuous geometric-average setup and assumptions; it does not explain how the formulas change for discrete averaging, dividends, or other market models.

Key ideas

  • A floating-strike geometric Asian call can be priced through a symmetric relation to a fixed-strike put.
  • The note provides closed-form expressions for floating-strike calls and puts under its stated setup.
  • The formulas assume a stock without dividends and use maturity, interest rate, and volatility inputs.
  • The document does not derive the formulas or discuss alternative averaging conventions.

Tags

OptionsDerivatives pricing
Full text
# Floating Strike Geometric Averaged Asian Option Pricing


# Floating Strike Geometric Averaged Asian Option Pricing












How can I use the risk neutral evaluation to price an asian option with floating strike using the continuous geometric average? I have tried searching for ways to do it but have found almost nothing.

## Answer by nachofest (score 1)

https://quant.stackexchange.com/a/75331

As Nick suggested, looking Espen G. Haug. The Complete Guide To Option Pricing Formulas. Mc- Graw Hill, 2007. P. Zhang. Exotic options, equation 4.105 shows a symmetric relation between a floating strike call and a fixed strike put. The latter is straightforward to calculate and using the substitutions for a fixed put with $S=S,X=S,T=T,r=0,b=-r,v=\sigma$ for a stock price with no dividends we obtain:

$V^{call}_{floating}(S,t=0) = SN(-d_2)-Se^{\frac{-T}{2}\left(r+\frac{\sigma ^2}{6}\right)}N(-d_1)$

using: $$d_1 = \frac{\frac{-1}{2}(r-\frac{1}{6} \sigma^2)T}{\sigma \sqrt\frac{T}{3}}$$ $$d_2 = d_1 -\sigma \sqrt \frac{T}{3}$$

And therefore: $$V^{put}_{floating}(S,t=0) = Se^{\frac{-T}{2}\left(r+\frac{\sigma ^2}{6}\right)}N(d_1)- SN(d_2)$$

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.