Questions tagged [asian-option]
The asian-option tag has no usage guidance.
30
questions with no upvoted or accepted answers
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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 $...
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votes
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91
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Option pricing boundary condition
I am currently working on this paper "https://arxiv.org/abs/2305.02523" about travel time options and I am stuck at Theorem 14 page 20. The proof is similar to Theorem 7.5.1, "...
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3
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180
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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^{...
- 31
2
votes
0
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208
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Monte Carlo Greeks for Fixed Strike Asian Call
I am interested in pricing an European-style fixed strike asian call with payoff $\max(A(S)-K;0)$, where $A(S)=\frac{1}{n}\sum_{i=1}^nS(t_i)$ is a discrete arithmetic average and $K$ is the strike ...
- 491
2
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83
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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 ...
- 1,086
2
votes
0
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144
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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 ...
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2
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157
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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}
\...
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1
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29
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Finite difference methods for an Asian call with boundary conditions
I have a question please.
I have to find the price of a Asian call using a finite diffenrece method.
Here the article, if u want to look it up, it's page 2-4: "https://www.researchgate.net/...
1
vote
0
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69
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Who knows what the name of this put option is? It's like a conditional Asian option, but with an upper boundary
Let $a < K < b$, then this option formula is:
$$\left(K - \frac{1}{\int_0^T\mathbb{1}_{\{a<S_t<b\}}dt}\int_0^TS_t\mathbb{1}_{\{a<S_t<b\}}dt\right)^{\large+}$$
1
vote
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60
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asian geometric option valuation-- unable to get monte carlo simulation to converge to analytic value
I'm trying to price asian put options in which the averaging window begins immediately (T=0). currently, I'm trying to match up geometric averaging between my Monte Carlo simulations and my attempt at ...
- 11
1
vote
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173
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Closed-form equation for geometric asian call option
I'm looking to use the geometric asian option as a control variable for a monte carlo simulation. However, I have an issue with the closed-form equation to get the geometric price.
I'm using the ...
- 11
1
vote
0
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204
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Asian option analytical approximation
I'm trying to approximate the price of an Asian option via the Black-Scholes formula by considering the discrete arithmetic average as a log-normal distribution.
$$
A_{T}(n):=\frac{1}{n} \sum_{i=1}^{n}...
- 11
1
vote
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210
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Pricing Asian and barrier option using Quantlib
I am exploring to use the ql.FdBlackScholesAsianEngine and ql.FdBlackScholesBarrierEngine using python code to price commodity options with implied volatility from traded European or American options. ...
1
vote
0
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69
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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-\...
- 221
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vote
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33
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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 ...
1
vote
0
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87
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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 ...
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1
vote
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185
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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 ...
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45
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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
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160
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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 ...
- 133
1
vote
0
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81
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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 ...
- 2,995
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380
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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 ...
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683
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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., ...
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51
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Different notations for times variable in Haug's book
I am reading the book by Haug, 2007 on the pages 186-188 one can find the Turnbull and Wakeman approximation for arithmetic avarage rate option.
The approximation adjusts the mean and variance so ...
- 253
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190
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Asian option equation
Im trying to find an equation for the discrete geometric asian option put price and are seeing a lot of differencies. Any recommondations for good papers??
I also tried to proof the call price from ...
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60
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Commodity forward curve Monte-Carlo
I need to value an Asian commodity option using Monte Carlo and a log-normal model. The inputs are the commodity forward curve and the volatility surface for futures/options expiry. Unfortunately, all ...
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51
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Effect of number of monitoring points on Asian Option Price
I want to understand conceptually the expected effect of the number of monitoring points used during the average calculation on Asian options pricing and the reason of such effect.
Asian Options ...
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52
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Why is the argument for the accumulated price process allowed to be negative in asian options?
Consider an Asian call option on some underlying with price process $S$ which follows a geometric Brownian motion, and accumulated price process $Y$, where
$Y_t = \int_{0}^{t}S_u du$. Let $v$ be the ...
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101
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Brownian Bridge from timestep 1 to timestep @ expiration, proper mathematical way to generate
When I was learning finance, we didn't cover the subject of Brownian Bridges. So I am trying to learn the proper way of generating paths when you have an arithmetic Asian option which has an ...
- 137
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148
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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
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0
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506
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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 $Y_t$?
...
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