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15 votes
Accepted

Path-dependent options valuation

Risk-neutral pricing A time-$T$ payoff is an integrable, $\mathcal{F}_T$-measurable random variable $\xi$. The value process of the discounted payoff is then a $\mathbb{Q}$-martingale, i.e., \begin{...
Kevin's user avatar
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6 votes
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How to perform Monte-Carlo simulations to price Asian options?

Instead of simulating the spot price, simulate its logarithm since the latter can be simulated exactly for any time step. \begin{equation} \ln S_{t + \Delta t} = \ln S_t + \left( r - \frac{1}{2} \...
LocalVolatility's user avatar
5 votes
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Asian Options-Change of Numeraire

Let $\mathbb{Q}$ be the risk-neutral probability measure which uses the risk-free bank account $(B_t)$ as numeraire. In general, $\mathrm{d}B_t=r_tB_t\mathrm{d}t$. In the Black-Scholes setting, $r_t\...
Kevin's user avatar
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4 votes

Is there any useful links for option pricing (american + asian + european) using R

Below is an example of how you could plot a "call" option value with RQuantLib: ...
zer0hedge's user avatar
  • 1,704
4 votes

Asian option sensitivity

For the Geometric Average Asian Option in BS, there is an arithmetic formula for the price - in fact, it is possible to price it using a BS vanilla options calculator, if you adjust the parameters ...
StackG's user avatar
  • 3,036
4 votes

What are some liquid Asian options markets?

I would guess options on FedFund futures are the world's most liquid Asian options. Here is the spec for FedFund futures: https://www.cmegroup.com/trading/interest-rates/stir/30-day-federal-...
piterbarg's user avatar
  • 940
4 votes
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Pricing PDE of Asian option by Shreve

Intuitively, once a stock hits value zero the underlying company is bankrupt and the value remains zero (this might not be true in the real world but it's a common assumption). So, once $S_t$ is zero ...
Bob Jansen's user avatar
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3 votes
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Continuous Geometric Asian Options

Whether arithmetic or geometric averaging, you always get \begin{align*} \mathrm{AsianCall} - \mathrm{AsianPut} = e^{-rT} (\mathbb{E}[\bar{S}]-K). \end{align*} So, let’s compute the expectation. You ...
Kevin's user avatar
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3 votes
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Asian Options Vs Bermudan Options

Asian options are more common in the FX market where corporate hedgers are concerned with the average exchange rate that affects regular streams of foreign denominated revenue. Bermudan exercise is ...
RRL's user avatar
  • 3,700
3 votes
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Unable to find Price of Asian Option using Explicit Finite Difference Method by implementing QuantLib in Python

QuantLib does have an FD pricing engine for asian options ql.FdBlackScholesAsianEngine(stochProcess, tGrid=100, xGrid=100, aGrid=50), but I've just discovered it ...
StackG's user avatar
  • 3,036
3 votes

Which stock tick has its geometric asian call?

They are not traded, even Over-The-Counter (OTC). Asian options with arithmetic averaging are traded. The geometric Asian may be used to derive a closed-form approximation for the arithmetic variety,...
jherek's user avatar
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3 votes
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Which stock tick has its geometric asian call?

Asian options are based on the average price of something during a period. The average price of a stock is not very interesting, so Asian options on stock are not traded. The average price of oil (...
Alex C's user avatar
  • 9,382
3 votes

Which stock tick has its geometric asian call?

This is an example of an exotic option. These are not listed and traded on any exchange. Rather they are traded in what is called the over the counter market. The dealers will trade these by entering ...
AlRacoon's user avatar
  • 6,632
3 votes

Asian Call Option

If $W$ is a standard Brownian motion then $\frac{1}{T}\int_0^T W_t dt$ has standard deviation $\sqrt{\frac{T}{3}}$. For this reason if $S_t=S_0e^{(\alpha -\frac{1}{2}\sigma^2)t + \sigma W_t}$ is the ...
Antoine Conze's user avatar
3 votes
Accepted

Pricing an Asian style forward contract with early exercise feature

Welcome to Quant SE. Unfortunately there is no closed form formula for computing the american contract value $\max_{\tau}E^P\left[e^{-r\tau}(A_{\tau} - K)\right]$, so you have to resort to an american ...
Antoine Conze's user avatar
3 votes

I have an interview for an assistant trader, need your help with some questions

On Question 1, you have zero delta (since you delta hedge) and negative gamma. So the cases where you lose money are (1) large upward movement of the underlying, (2) large downward movement of the ...
Alex C's user avatar
  • 9,382
3 votes

Simulation of the Vega in Heston model (for Asian Option)

Chan, Jiun Hong and Joshi, Mark S. and Zhu, Dan, First and Second Order Greeks in the Heston Model (December 26, 2010). Available at SSRN: https://ssrn.com/abstract=1718102 or http://dx.doi.org/10....
Mark Joshi's user avatar
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3 votes

How to perform Monte-Carlo simulations to price Asian options?

Kemna and Vorst (1990) [ download ] is a classic in Monte Carlo method for Asian option. Geometric mean, which can be analytically computed, is used as a control variate to reduce MC noise.
jChoi's user avatar
  • 1,174
2 votes

How to perform Monte-Carlo simulations to price Asian options?

Looks good to me, although idk why you have (T-t) in the discounting... isn't big T the total time to maturity? What is little t in the equation? Shouldn't it just be exp[-rT] because you discount ...
Alex Ockenden's user avatar
2 votes
Accepted

Turnbull & Wakeman Asian - not Edgeworth?

Yes, AFAIK, they used Edgeworth expansions [ download ] The objective of this paper is to describe a quick way to price European average options. While it is very difficult to determine the ...
jChoi's user avatar
  • 1,174
2 votes

Implied Volatility for Asian option

The approximation I mentioned earlier is that in order to price an Asian option with strike K and maturity T on an asset with spot price S0, one should use the implied volatility at the modified ...
danp's user avatar
  • 116
2 votes
Accepted

Asian option and option pricing

This is the standard textbook definition for the payoff of an arithmetic average Asian call option. In reality the average will be based on a daily average of stock prices over some period at the ...
Dom's user avatar
  • 2,167
2 votes

Black 76 and Asian Style Options on Shaped Power Futures

I think to answer your question, it needs to be understood accurately how the option contract that you are pricing is defined. If you are looking at a pay-as-produced type option, you also need to ...
ZRH's user avatar
  • 1,671
2 votes

What are some liquid Asian options markets?

Asian options are the most liquid markets for options on commodities which are delivered over time such as electric power and natural gas. Some metal smelters also use Asian options since their plant ...
kurtosis's user avatar
  • 2,910
2 votes

Monte Carlo for Asian Pricing

The paper is reliable and the formula is correct. However as you mention yourself there is an error. $$ \frac{\log \left(\frac{e^{0.01}-1}{0.01}\right)}{0.01} = 0.500417 \neq 0.498 $$
Sanjay's user avatar
  • 1,667
2 votes

Pricing of Asian-like option

It would be an Asian strike call option, with the Asianing being computed over some period $[0;\tau]$. Not a big deal that the average is not computed from 0 to T. It even seems more natural to be ...
Soumirai's user avatar
  • 624
2 votes
Accepted

Sum of discretely sampled BM

We have $S_t = \sigma S_tdW_t$ and $A_N = \sum_{n=1}^N S_n = S_0\sum_{n=1}^N e^{\sigma W_n-\frac12\sigma^2n}.$ $$\mathbb E[A_N] = S_0\sum_{n=1}^N \mathbb E[e^{\sigma W_n-\frac12\sigma^2n}] = NS_0.$$ $$...
LucaMac's user avatar
  • 241
2 votes

What is the meaning of an implied volatility of an Asian option?

Practitioners use Monte Carlo methods, the moment matching method (Levy approximation) and when they want to be super-precise, the Curran method.
danp's user avatar
  • 116
2 votes
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SABR LMM vs no-arbitrage term structure of SABR parameters

I am guessing that the first model you are referring to is the one from Rebonato: Linking caplets and swaptions prices in the LMM-SABR model (2009)? If yes, then I would say that your approach is a ...
BEQuant's user avatar
  • 428
1 vote

Unable to find Price of Asian Option using Explicit Finite Difference Method by implementing QuantLib in Python

Using MC Simulation, if I am trying to price Geometric Average Asian Option by running the following code: ...
Desi_Quant's user avatar

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