Questions tagged [asian-option]

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Exotic options with lookback features [closed]

I am trying to value an american call option with a lookback feature. So the holder can choose to exercise either based on a fixed strike (K) or a floating strike equal to 10-day moving average (MA). ...
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1 vote
1 answer
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SABR LMM vs no-arbitrage term structure of SABR parameters

There exists a LIBOR Market Model with stochastic volatility for pricing and hedging exotic (e.g. path-dependent) interest rate options with smile. However let us consider the following approach: ...
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1 answer
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What is the meaning of an implied volatility of an Asian option?

Suppose that an Asian option is quoted OTC in terms of its implied volatility. What is the meaning of an implied volatility in this case? Is it an implied volatility of a vanilla European option with ...
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Implied volatility surface of an average rate Asian caps

Lets say I have a SABR model where implied volatility is given by semi-analytical Hagan et al. formulas and individual caplets are priced with analytical Black formulas. This model allows me to ...
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4 votes
2 answers
399 views

Asian option IV less than vanilla option IV

I was wondering whether the following handwaving line of thought can be used to show that the IV of an Asian option is less than the IV of a vanilla option with the same strike and time to maturity: ...
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0 votes
0 answers
41 views

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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Pricing asian options with Monte Carlo and brownian bridge

I am trying to price arithmetic asian options using Monte Carlo method and a brownian bridge construction. My code does not seem right as the price with a geometric conditioning gives me a price of 5....
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1 vote
0 answers
103 views

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}...
0 votes
1 answer
106 views

Understanding the expected value of the average

I've been looking into Asian Options pricing. Part of the process is about looking for the expected value of the average of a time series undergoing e.g. geometric brownian motion. I came across this ...
0 votes
1 answer
168 views

Discrete geometric asian option call price formula

I am looking to derive the call price of an asian option of the form $$\max\{A_T - K, 0\}$$ with $$A_T = \left(\prod_{i=1}^nS_{t_i}\right)^\frac{1}{n}$$ which has price under $\mathbb{Q}$ $$e^{-rT}[...
0 votes
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57 views

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 ...
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1 vote
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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. ...
2 votes
1 answer
161 views

Interpreting Implied Volatility in Commodities Options

I understand that implied volatility is the expected volatility of an underlying contract in the Black option pricing model. This is easy to interpret for assets delivered at a point in time. But how ...
2 votes
0 answers
123 views

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 ...
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8 votes
1 answer
508 views

Path-dependent options valuation

Assume that we have an arbitrage-free and complete market. The well known formula for the arbitrage-free price of an attainable derivative $X$ at time $0 \leq t \leq T$ is given by: \begin{align*} V(t)...
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2 votes
1 answer
121 views

FX Asian Option Moment-matching in Harmonic case

I need to price a "foreign-paying" fixed-strike Asian (i.e., average) option. Thus, the payoff is: $$\left(\frac{A_T - K}{A_T}\right)^{+} = \left(1 - \frac{K}{A_T}\right)^{+} = K \left(\frac{...
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112 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
1 answer
103 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 $A_N$?
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1 vote
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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 ...
2 votes
2 answers
356 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
1 answer
329 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
0 answers
64 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-\...
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4 votes
0 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 $...
2 votes
1 answer
199 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\...
1 vote
2 answers
419 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
1 answer
195 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 ...
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2 votes
0 answers
80 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 ...
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2 votes
1 answer
214 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}...
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2 votes
1 answer
238 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 ...
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1 vote
1 answer
427 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; ...
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2 votes
0 answers
104 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
1 answer
112 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 ...
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1 vote
1 answer
305 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
0 answers
33 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 ...
5 votes
1 answer
195 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 ...
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2 votes
0 answers
117 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
1 answer
357 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
1 answer
128 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
3 answers
126 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 ...
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1 vote
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70 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 ...
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1 vote
0 answers
164 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
0 answers
37 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
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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 ...
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1 vote
0 answers
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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 ...
0 votes
1 answer
164 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
0 answers
481 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
1 answer
1k 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
1 answer
332 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
1 answer
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 ...
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1 vote
0 answers
333 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 ...