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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, "...
Valentin's user avatar
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2 votes
1 answer
148 views

Pricing PDE of Asian option by Shreve

I am currently working on "Stochastic Calculus for finance II, continuous time model" from Shreve. In chapter 7.5 Theo 7.5.1 he derives a pricing PDE with boundary conditions for an Asian ...
Valentin's user avatar
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1 answer
82 views

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 ...
Nick's user avatar
  • 253
1 vote
0 answers
33 views

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/...
Raphael Morel's user avatar
1 vote
1 answer
274 views

Hedging exotic options

How can exotic and other path dependent, such as asian options be hedged? For example in the case of an asian option, what is the replicating portfolio: what instruments to keep in it and “how much”? ...
Kapes Mate's user avatar
0 votes
0 answers
232 views

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 ...
Halmo's user avatar
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1 vote
0 answers
69 views

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: $$\left(K - \frac{1}{\int_0^T\mathbb{1}_{\{a<S_t<b\}}dt}\int_0^TS_t\mathbb{1}_{\{a<S_t<b\}}dt\right)^{\large+}$$
Peanut Hunter's user avatar
0 votes
0 answers
68 views

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 ...
Sergey Chigrinov's user avatar
1 vote
0 answers
62 views

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 ...
donpicante's user avatar
1 vote
0 answers
236 views

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 ...
Vpaq's user avatar
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52 views

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 ...
nachofest's user avatar
1 vote
0 answers
38 views

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). ...
DLW's user avatar
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1 vote
1 answer
269 views

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: ...
Hasek's user avatar
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1 answer
304 views

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 ...
Hasek's user avatar
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4 votes
2 answers
478 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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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 ...
BaroqueFreak's user avatar
1 vote
0 answers
208 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}...
Asopanap's user avatar
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1 answer
195 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 ...
Experience111's user avatar
0 votes
1 answer
782 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}[...
SimonCello94's user avatar
0 votes
0 answers
109 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 ...
Matt's user avatar
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1 vote
0 answers
212 views

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. ...
Quant enthsiast's user avatar
2 votes
1 answer
229 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 ...
CasusBelli's user avatar
2 votes
0 answers
213 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 ...
Count's user avatar
  • 491
9 votes
1 answer
853 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)...
Count's user avatar
  • 491
2 votes
1 answer
195 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{...
X Y's user avatar
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0 votes
0 answers
154 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 ...
quant_student's user avatar
0 votes
1 answer
104 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 $A_N$?
Toby1729's user avatar
1 vote
1 answer
100 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 ...
CasusBelli's user avatar
2 votes
2 answers
697 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 ...
Richard Hardy's user avatar
1 vote
1 answer
560 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-...
david.t_92's user avatar
1 vote
0 answers
70 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-\...
Parseval's user avatar
  • 221
4 votes
0 answers
135 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 $...
user107224's user avatar
2 votes
1 answer
373 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\...
user107224's user avatar
1 vote
2 answers
713 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 ...
Desi_Quant's user avatar
3 votes
1 answer
366 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 ...
Bogaso's user avatar
  • 836
2 votes
0 answers
83 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 ...
Freelunch's user avatar
  • 1,086
2 votes
1 answer
255 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}...
Anon's user avatar
  • 281
2 votes
1 answer
319 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 ...
Anon's user avatar
  • 281
1 vote
1 answer
647 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; ...
Anon's user avatar
  • 281
2 votes
0 answers
152 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 ...
Dhruv Mahajan's user avatar
2 votes
1 answer
165 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 ...
Wenzel's user avatar
  • 23
1 vote
1 answer
412 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 ...
OvermanZarathustra's user avatar
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 ...
Ashish Ranjan's user avatar
5 votes
1 answer
237 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 ...
Henry P's user avatar
  • 51
2 votes
0 answers
158 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} \...
foreignvol's user avatar
3 votes
1 answer
501 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 ...
Leslie Wu's user avatar
1 vote
1 answer
174 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 ...
Leslie Wu's user avatar
0 votes
3 answers
132 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 ...
kenneth's user avatar
  • 167
1 vote
0 answers
88 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 ...
McAsia's user avatar
  • 11
1 vote
0 answers
186 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 ...
user6703592's user avatar