Questions tagged [asian-option]
The asian-option tag has no usage guidance.
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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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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:
$$\left(K - \frac{1}{\int_0^T\mathbb{1}_{\{a<S_t<b\}}dt}\int_0^TS_t\mathbb{1}_{\{a<S_t<b\}}dt\right)^{\large+}$$
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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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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 ...
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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 ...
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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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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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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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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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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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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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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.
$$
A_{T}(n):=\frac{1}{n} \sum_{i=1}^{n}...
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157
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Understanding the expected value of the average
I've been looking into Asian Options pricing. Part of the process is about looking for the expected value of the average of a time series undergoing e.g. geometric brownian motion.
I came across this ...
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Discrete geometric asian option call price formula
I am looking to derive the call price of an asian option of the form
$$\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}[...
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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 ...
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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. ...
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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 ...
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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 ...
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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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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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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 ...
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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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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 ...
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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 ...
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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-...
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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-\...
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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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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\...
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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 ...
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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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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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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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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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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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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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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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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 ...
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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 ...
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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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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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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 ...
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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 ...
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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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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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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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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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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 ...
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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?
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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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