Questions tagged [basket]

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Cross Gamma PnL Formula

sort of dumb question. I understand well the relationship between Gamma/Theta pnl for options on single underliers. I'm (attempting) to move onward and upward to options on baskets. Conceptually, I ...
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1 answer
92 views

Has anyone ever derived an analytical basket option which gives terminal asset prices individually, by asset?

Random thought I had around what would be an ideal analytical basket formula. If the formula gave terminal prices of each asset instead of a single basket price, you could price any number of exotic ...
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62 views

Is this the right way to accelerate my Monte-Carlo Simulation

I am trying to develop a pricer for Call VS Call and I'm using MonteCarlo method to do so because my stocks are correlated between each others. Basically my inputs are ...
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1 vote
0 answers
58 views

Extend basket analytic solution (equal weighted) to a various weight basket, also put formula

So I coded up the solution from here: Do basket options have a closed form valuation formula? Which provides a good solution for equally-weighted underlyings under a Black model. The simplified ...
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1 vote
0 answers
57 views

Volatility of basket with constituents priced in different currencies

I'm wondering how the volatility of basket of constituents priced in different currencies can be calculated (without upfront bringing constituent price to basket currency) form volatilities of ...
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0 votes
1 answer
132 views

Basket option: volatility surface

I would like to calculate a basket European option with Black Scholes local volatility model. I want to simplified the basket option into a single underlying European option. Should we get the local ...
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1 answer
366 views

Does anyone have any suggestions on using Monte Carlo simulations to calculate Greeks of basket option?

I'd ideally like to use algorithmic differentiation or finite difference methods to approximate the Greeks of a basket option. It would be a European style basket on $N$ stocks with the payoff being $\...
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2 votes
3 answers
898 views

Do basket options have a closed form valuation formula?

Suppose I'm simulating a European call option on a basket consisting of N stocks with slightly varying volatilities but all other parameters remain the same. From the perspective of an estimate, it ...
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2 votes
0 answers
74 views

Estimate of basket volatility

We are looking for a simple way to calculate an approximation of the basket volatility for a set of baskets so that we can estimate which basket might produce the highest coupon in a standard ...
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2 votes
1 answer
208 views

Monte carlo delta calculation for Worst/Best Of Option

I try to calculate the Delta for WO by finite difference. For example, $K = 1.$ $$ S_t = S_0 e^{(r - d_1 - \frac{\sigma_1^2}{2})t + \sigma_1 W_t^1} $$ $$ F_t = F_0 e^{(r - d_2 - \frac{\sigma_2^2}{...
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117 views

0 Delta on Forward starting Equity basket option

I wanted to confirm the inherent reasoning behind 0 delta on a weighted equity basket option. For instance, if we have a basket option with a forward starting initial fixing date, we can expect the ...
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1 vote
0 answers
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What is the name of these digital basket options?

Consider a basket of correlated assets $(S_1(t),\ldots, S_N(t))$, as well as a vector of strike prices $(K_1,\ldots,K_N)$, and let's look at the following European payoff types: An option that pays 1€...
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2 votes
1 answer
126 views

Nearly replicate a basket with a few of its constituents

Motivation I have a basket with 30 constituents each with a weight which I want to nearly replicate with less than 30 trades for reducing trading costs. Better definition Better replication equals ...
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1 answer
192 views

Barrier option on a basket with arbitrary stochastic process

Suppose I want to price a Down-and-out European call, barrier option. However, the stochastic process is not a gBm or any other Levy process with known structure. Practically, I want a barrier option ...
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4 votes
0 answers
1k views

Volatility of a stock basket

to determine the volatility of a basket of stocks, I often use the following formula: $\sigma_{basket}=\sum_{i}\sum_{j}w_i w_j \sigma_i \sigma_j \rho_{ij}$ where the $\sigma$ are the constituents' ...
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1 vote
0 answers
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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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3 votes
1 answer
530 views

Correlation basket equities

One question: when asking for the correlation of a basket, a trader told me 50% whereas I expected him to give me asset pairwise correlations (i.e. the correlation matrix). What does this 50% mean ...
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2 votes
1 answer
252 views

QuantLib: How to change polynomial order in MCAmericanBasketEngine?

My goal is to price American basket put options using the Least squares Monte Carlo, or Longstaff-Schwartz algorithm. I currently have the one-dimensional case working with the Python file below (I ...
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1 vote
1 answer
600 views

Software for American basket option pricing using Longstaff-Schwartz/Least Squares Monte Carlo method

Is there free software (preferably in Python) that computes American basket (high-dimensional!) option prices in the Black Scholes model using the Longstaff-Schwartz algorithm (also known as Least ...
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  • 153
5 votes
2 answers
757 views

Difference between Local Vol and Copula

Let's assume we have ATM European call on a basket of two stocks and price it with: 1) Multivariate Local Vol with constant correlation 2) Gaussian copula Assuming we use the same correlation ...
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1 vote
1 answer
2k views

Basket Option pricing of two stocks

I am trying to use Monte Carlo simulation to price arithmetic basket option consisting of two stocks. There seems to be something wrong in my implementation. According to the inputs ...
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4 votes
2 answers
724 views

Smoothing of the payoff function as a terminal condition for numerical option pricing

I am interested in using a 4th order finite difference method in (underlying asset) space to price a European call basket option. I have developed the solver and everything works as expected, except ...
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5 votes
1 answer
2k views

How to price this basket option?

Underlying assets are three global stock index : Eurostoxx 50, HSI, KOSPI 200 Maturity: 36 months with advanced redemption date in every 6 months if prices of indexes satisfy given conditions at each ...
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5 votes
3 answers
231 views

Basket derivatives on weather AND financial underlying?

Is somebody aware whether there exist basket derivatives whose underlyings are either related to weather (e.g. temperature) or financial indices (e.g. S&P500)? It is essential that the payoff ...
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5 votes
0 answers
1k views

Greeks of a Basket Option

I want to estimate delta, vega and gamma for a basket option. This option is a European Call option. The underlying is $S=\omega_1 S_1 +\omega_2 S_2$ Where: $S1$ = stock price of asset 1 $S2$ = ...
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3 votes
1 answer
156 views

Pricing homogeneous Basket Default Swap

Consider a basket with $K=10$ names. Default times of the names, $\tau_k$, are i.i.d. random variables with distribution $P(\tau_k \leq t) = 1 - e^{-\lambda t}$. Suppose that each name in the basket ...
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1 vote
0 answers
122 views

Construction of bond portfolio represented by a CDS-Index

Markit publishes investable basket CDS indices. These are indices intended to track the credit risk of a basket of issuers (e.g. in the case of iTraxx Europe Series 24 these are 125 names) in an ...
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5 votes
1 answer
3k views

How to calculate implied volatility smile of basket using correlations?

For a basket, the realized volatility can be calculated using: $$\sqrt{\sigma_1^2 + \sigma_2^2 + 2 \sigma_1 \sigma_2 \rho}$$ If I have the volatility surface of two underlyings S1,S2 (strike space). ...
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3 votes
0 answers
103 views

Basket Default Swap (BDS)

I would like to understand better the $n^{th}$ to default pair spreads of a basket default swap containing $m>n$ entities. For example, consider 2 single name CDS's with same spread and same ...
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0 votes
1 answer
352 views

Finding historical data for indices [duplicate]

Where can I find historical data for option prices on a given index ? Ideally I'd like to find for a period of several months 1) historical prices on options on a given index 2) historical prices on ...
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8 votes
2 answers
841 views

Looking for Research Paper on Creation of Currency Baskets

I came across a paper, not sure it originated from academia or a blog or such, that reported on applying principal components to build currency baskets from a set of individual currency pairs and to ...
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1 vote
0 answers
164 views

What are the industry standard models for monte carlo simulation of basket options?

I would like to simulate an equity index, a risk free cash account and the yield curve for the purposes of valuing a guarantee on an insurance product that is being backed by both equities and cash. ...
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8 votes
0 answers
234 views

Basket option density in BS model

Let X and Y be two GBM’s, they have each a univariate log-normal distribution for some time t, that is $X_t\sim{LnN(µ_x, σ^2_x)}$, $Y_t\sim{LnN(µ_y, σ^2_y})$ and $Z_t=[X_t,Y_t]\sim{ MvLnN(μ, Σ)}$ ...
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2 votes
1 answer
983 views

Greeks of Basket

I am considering a product composed of 10 underlying assets. The maturity is 5 year. Each year if the performance of the equi-weighted portfolio reach a barrier, it pays a coupon. My question concern ...
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5 votes
1 answer
3k views

what is the implied volatility on a basket of options

If I have 4 optionable stocks A,B,C,D and each different implied volatilies,IV-A,IV-B,IV-C,IV-D. How do get the implied volatility for a basket option on A,B,C,D where the basket weights are w-A=.6, ...
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8 votes
4 answers
9k views

Basket option pricing: step by step tutorial for beginners

I would like to learn how to price options written on basket of several underlyings. I've never tried to do it and I would appreciate if you can provide some documents, papers, web sites and so on in ...
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6 votes
0 answers
526 views

Taking into account the correlation in Barrier options on a Basket

In a Barrier option (where the contract cancels when the underlying hits the barrier) I succesfully found the way to compute the probability of a single underlying touching the barrier (with constant ...
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15 votes
2 answers
2k views

Can you replicate an option on an arbitrary basket of stocks?

Since a market index is nothing more than a basket of stocks, you can create your own index by putting together stocks of your choice. The only difference is that you can trade options on major ...
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10 votes
2 answers
2k views

Why does this Co-integrated basket look too good to be true?

You need quantmod & tseries in R to run this: ...
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