Questions tagged [asian-option]

The tag has no usage guidance.

Filter by
Sorted by
Tagged with
0
votes
0answers
59 views

Discrete geometric asian option, analytic vs MC

I am attempting to price a discrete geometric Asian option using both the closed form formula (can be found in section 3.2.2 of 'Monte Carlo methods in Financial Engineering' by Glasserman) and an MC ...
0
votes
1answer
96 views

Sum of discretely sampled BM

If an underlying follows lognormal GM with no drift $dS_t = \sigma S_t dW_t $ and $A_N = \Sigma_{i=1}^{N} S_{t_i}$. How to compute variance of $A_N$?
1
vote
0answers
24 views

Black 76 and Asian Style Options on Shaped Power Futures

I am attempting to price a monthly lookback option on the gen-weighted average price of power at a particular solar plant over a given month. If the option settles at hub H, am I right to shape the ...
0
votes
0answers
33 views

The put-call parity have to be fulfilled by an asian option

Coming from here: https://quant.stackexchange.com/a/7616/43679 we have that for a European option, and due to the put-call parity, due to the non arbitrage rule, the volatility for a put and a call ...
1
vote
2answers
156 views

What are some liquid Asian options markets?

I have some ideas about Asian options that I would like to test with historical market data. I am therefore looking for some fairly liquid Asian options markets, preferably ones with publicly ...
1
vote
1answer
90 views

Greeks for Asian options on futures

I'm trying to get the Greeks for the PDB Option Contract (Crude Outright - Dated Brent (Platts) Average Price Option): https://www.theice.com/products/26535747/Crude-Outright-Dated-Brent-Platts-...
1
vote
0answers
54 views

Show that stochastic integral is $F_W(t)-$measurable

In some notes, my professor writes the following for the price function of an geometric asian option: \begin{align} \text{Price}(t)&=\tilde{\mathbb{E}}\left[\left(S(0)\exp\left(\frac{T}{2}\left(r-\...
4
votes
0answers
92 views

Pricing of strange Asian lookback option with European-style payoff $\max\{ \max_{u\in[0,T]}S_u-\frac1T\sqrt{\int_0^TS_t^2\mathrm{d}t},0\}$

I am trying to price the Asian lookback option at time $t$ with time-$T$ (European) payoff $\max\{M_T-A_T,0\}$, where $$M_t=\max_{u\in[0,t]}S_u,\quad A_t=\frac1t\sqrt{\int_0^tS_u^2\mathrm{d}u},$$ and $...
2
votes
1answer
142 views

Pricing of Asian-like option

I am considering an option which has payoff function $\max\{S_T-\frac1\tau\int_0^\tau S_t\mathrm{d}t,0\}$ for a fixed $\tau$ in the risk-neutral measure $\mathrm{d}S_t/S_t=r_t\mathrm{d}t+\sigma_t\...
0
votes
0answers
94 views

Discrete Geometric Average Methodology for Pricing Asian Option using Finite Difference in Python

I am able to price Asian Options using Discrete Arithmetic Average in Finite Difference scheme and implementing the same in Python. However I am struggling to write the code for the same in Discrete ...
1
vote
2answers
132 views

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

I am trying to find price of Continuous Geometric Average Asian Option using Finite Difference methodology in QuantLib Python. I am unable to do so. However, I am able to find price of the same option ...
3
votes
1answer
116 views

Asian option sensitivity

I am looking for some materials for profiling all options sensitivities for Asian options with both geometric averaging and arithmetic averaging . The underlying price $S_t$ follows a standard GBM. Is ...
2
votes
0answers
69 views

Average Strike Option with bounds

I'm looking to price a call option with an exotic feature. The price I'm trying to calculate at time $t=0$ is \begin{equation} C = E^\mathbb{Q}[(S_T-K_T)^+] \end{equation} where $S_t$ is the stock ...
2
votes
1answer
187 views

Arithmetic Asian Option

Assume the risk-free bond Bt and the stock St follow the dynamics of the Black & Scholes model without dividends (with interest rate r, stock drift $μ$ and volatility $σ$). Let $A_T:=\frac{1}{T}...
2
votes
1answer
176 views

Asian Options-Change of Numeraire

Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model without dividends (with interest rate r, stock drift $\mu$ and volatility $\sigma$). Show that ...
1
vote
1answer
297 views

Continuous Geometric Asian Options

Assume the risk-free bond $B_t$ and the stock $S_t$ follow the dynamics of the Black & Scholes model without dividends (with interest rate r, stock drift $\mu$ and volatility $\sigma$). Let $c(t; ...
2
votes
0answers
76 views

Stratified sampling in asian options

I am using the procedure of stratified sampling for variance reduction. In the Glasserman book the algorithm for stratified the terminal value of the Brownian motion is given for european options. For ...
1
vote
1answer
90 views

Is it possible to transform arithmetic-average strike continuous sampling Asian Black-Scholes equation to a heat equation?

By Transformation from the Black-Scholes differential equation to the diffusion equation - and back, we are able to transform vanilla European option into a heat equation. And we know that the ...
1
vote
1answer
184 views

Asian Options Vs Bermudan Options

Which of these options are more popular in practice/used in industry? And where exactly are they used? Also, I have been searching for listed Asian and Bermudan options, for volume data etc, but have ...
1
vote
0answers
32 views

Give the formula for following resulting portfolio process

Consider the continuously sampled a derivative security with payoff function $V(T) = \frac {\int_0^TS(u)du}T -K$ but assume now that the interest rate is $r=0$. Find an initial capital $X(0)$ and a ...
4
votes
1answer
150 views

Monte Carlo for Asian Pricing

I'm trying to verify the accuracy of my Monte Carlo method for pricing mean options. I came across this paper that supposedly gives an 'exact' solution for the arithmetic mean option (asian). It's a ...
2
votes
0answers
96 views

American-Bermudan-Asian option fixed strike using finite differences

I'm trying to price the same American-Bermudan-Asian option described in Longstaff Schwartz (2001). Specifically, using finite difference methods with an explicit scheme to solve $\begin{aligned} \...
3
votes
1answer
283 views

Pricing an Asian style forward contract with early exercise feature

Is there an analytic way to price or approximate a contract with payout $A_t - K$, where $A_t$ is the running average price of the underlying asset from $[0, t]$ and $K$ is (fixed) strike. If this ...
1
vote
1answer
104 views

Pricing American style Asian option

Is there any approximation of American style Asian option (with strike equal to the running averaging from 0 to $t$) pricing based on analytical closed form formula? I see the price difference ...
0
votes
3answers
112 views

Which stock tick has its geometric asian call?

Many finance books introduce the pricing on geometric asian call/put options underlying black-scholes model, since its price has its explicit formula. I am not sure, if geometric asian option is ...
1
vote
0answers
39 views

Asian basket option variance reduction control variates monte carlo

I have priced an Asian put option with three underlying correlated stocks. Now I want to try to reduce the variance using control variates. I have found great ideas when there is one underlying (thus ...
1
vote
0answers
139 views

Does the Asian Option (average Option) depend on the forward implied vol

I can easily understand that the forward starting Option and Barrier Option depend on the forward implied vol smile at resetting date, so we always choose the stochastic vol model for underlying to ...
1
vote
0answers
27 views

Convention for Discrete Asian / Lookback Options

When computing the Payoff of Discrete Asian / Lookback Options (say 12 observations) using MC, does one usually use the value of S0 as well or only the latter realisations? Best regards, Alex
1
vote
0answers
129 views

Pricing a Path-Dependent Option with Heston

I want to price a path-dependent option (let's say for example an arithmetic average Asian option) under a Heston model. In a Black-Scholes setup, I use forward volatilities to do so. I want to apply ...
1
vote
0answers
66 views

Probability distributions as solutions to differential equations

As far as what I can tell, the popularity of the Black-Scholes-Merton model partly stems from the fact that it formulates the value of a derivative in a differential form in which the solution has a ...
0
votes
1answer
144 views

Asian Call Option

An Asian call option with the average strike payoff, uses the “averaging” to reduce the effect of volatility. Why is this so?
0
votes
0answers
447 views

Time integral of geometric brownian motion

Suppose $S_t$ is a geometric brownian motion. Then how to understand its time integral, i.e., $Y_t=\int_0^{t}S_udu$? Is $Y_t$ still a stochastic process? How to compute the expectation of $Y_t$? ...
2
votes
1answer
970 views

Wrong pricing of Asian Option

Issue short: I have values for Asian Options which I'm trying to replicate using a self-build vba calculator. The values I have to hit is from FinCAD and I'm using a discrete arithmetic average rate ...
3
votes
1answer
271 views

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

I'm trying to evaluate option pricing mainly american, asian and european options in order to get a plot to measure option valuation in time. Is there any useful references to do that using R ?
-2
votes
1answer
3k views

Monte carlo simulation for arithmetic average price asian option [closed]

I am trying to construct a method in python that evaluates the value of an Arithmetic Asian Option using standard Monte Carlo simulation (without control variates). However, I am not getting the ...
1
vote
0answers
269 views

Pricing Asian option at discrete times

I hope you can help me again regarding pricing an arithmetic Asian option. Assume we have a time grid $(0=t_0,t_1,t_2=T)$ and we buy an Asian option at time 0 and the maturity is at T. Now we would ...
3
votes
1answer
468 views

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

I'm new here and I hope you guys can help me. I want to calculate/simulate the Vega for my Asian option in the Heston model. The only source I found is the paper of Broadie/Kaya (2004) but they just ...
6
votes
3answers
5k views

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

If I wish to price a fixed-strike Asian Call option via Monte-Carlo (This has no early-exercise), are my following steps correct?: 1) Simulate random asset prices. (Milstein) $\ d S(t) = \ rS(t)dt + ...
1
vote
1answer
326 views

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

Hello all hope you're doing fine! Would you please help me answering these questions? 1) We're short a call option and we delta hedge. We know that there will be a move in the underlying asset ...
1
vote
1answer
436 views

Asian option and option pricing

I know Asian option is defined as follow $$\left(\frac{1}{T}\int_{0}^{T}S_t dt-K\right)^+$$ Is there a good idea behind this definition. Thanks.
1
vote
1answer
433 views

Is Asian option in binomial asset pricing model a martingale?

Since it does not have a closed form solution for the price, it's unlikely to be a martingale. However, on the other hand, if we represent the price as a function of the current stock price and the ...
0
votes
1answer
707 views

Turnbull & Wakeman Asian - not Edgeworth?

My understanding is that Turnbull & Wakeman derived an approximation formula for continous arithmetic Asian option using Edgeworth series by matching the first two moments. However, in the book ...
3
votes
0answers
145 views

Approximate asian geometric option with Heston

I am trying to implement Theorem 1 from this Journal in RStudio. The journal says the it is possible to find a approximate price of a geometric asian option in a Heston setup this way: $$X_{1cGAO}=e^{...
2
votes
1answer
388 views

Negative adjusted strike in Levy's Asian option approximation?

In Edmond Levy's 1992 paper, he introduced a moment-matching method to approximate the price of an Asian option assuming GBM for the underlying. It suggested that, if some monitor points are already ...
4
votes
1answer
522 views

Asian Option with Geometric Averaging

Can someone point me to any notes on how to derive the closed form formula for Asian geometric average option with payoff $\text{max}\left(\text{log}\left(\frac{A_T}{K}\right), 0\right)$ where $A_T$ ...
6
votes
3answers
392 views

Price of an asian option with squared of average payoff

Is there a closed form solution of the following price formula? Assuming $dS_t=rSdt+\sigma S_t dW_t$ under the Q dynamics $e^{-r(T-t)}\mathbb{E}_t^\mathcal{Q}[(\frac{(\int_0^T S_u du)}{T})^2]$ I ...
7
votes
1answer
496 views

What is the mechanism of Asian option?

I have no problem with the mathematical definition of an Asian option. For example, assume the strike price is $K$, the expiration date is $T$, the underlying asset has price $S(t)$, and the payoff is ...
1
vote
0answers
648 views

Asian option numerical pricing method generates a negative time value

I use R to write a function which simulates price path and calculates the value of an arithmetic Asian option. I found sometimes the value of the option can be lower than its intrinsic value, i.e., ...
6
votes
1answer
588 views

Boundary condition for Asian Option under Black-Scholes model

I am looking at Kemna and Vorst's paper: A PRICING METHOD FOR OPTIONS BASED ON AVERAGE ASSET VALUES. see http://www.javaquant.net/papers/Kemna-Vorst.pdf Let $\text{d}S_t = S_tr\text{d}t + S_t\sigma\...
3
votes
2answers
244 views

What information about the stochastic process is available from path-dependent options?

Assume the stock follows a process, which is defined by the following stochastic differential equation $$\frac{dS}{S}=r(t)dt+\sigma(S,t)dW,$$ so that the stock price process has local volatility. ...