# Tag Info

9

The main problem in your code is this line: rowSums(coef(model) * frame[, -1]) I'm not sure exactly what is does, perhaps some matrix multiplication, but definitely not what you expect it to do. Try to replace it with manual multiplication spread <- frame[,1] - (coef(model)[1]*frame[,2] + coef(model)[2]*frame[,3] + coef(model)[3]*frame[,4] + coef(...

8

Interesting question. Unfortunately for you, the answer is no, it cannot be done. The principal difference between a basket of options and an option on the basket (or index) is correlation risk. In fact, there is a systematic difference between the implied volatility of the basket and the (properly weighted) sum of implied volatilities on the components. ...

5

No offense but it will be much more complicated than what you think... I'm not even sure that you are familiar with risk-neutral pricing in the first place? I'll try to give you some clues. This security is called a basket option. On top of the multi-asset feature, there are non-trivial mechanisms embedded in the contract you mention: an auto-callable ...

4

I think you should not just ask what the implied vol is of a basket of equity derivatives but you should aim to generate a volatility surface. A spot implied vol gives you nothing to work with. What you need is an implied vol surface in order to understand the smile and skew effects when you quote basket options in the market and/or as price taker. Take a ...

3

Let $\tau_{(1)} = \min(\tau_1, \ldots, \tau_K)$ be the first-to-default time. Moreover, for $1< m \le K$, let \begin{align*} \tau_{(m)} = \min\left(\tau_k: k=1, \ldots, K, \tau_{k} > \tau_{(m-1)}\right). \end{align*} be the $m^{\rm th}$-to-default time. In particular, $\tau_{(K)} = \max(\tau_1, \ldots, \tau_K)$. Note that, for $t \ge 0$, \begin{align*} ...

3

If you are looking for derivatives on weather (temperature, heating degree days, cooling degree days) and a financial "index", I think your best bet would be to look for hybrid weather/commodity derivatives.

3

@Sergey correctly identified the problem. The explanation is that coef(model) is a vector, frame is a data.frame, and element-by-element multiplication takes place in column-major order. The shorter vector (coef(model)) is recycled along the longer vector (each column in frame). For example: frame <- data.frame(V1=1:5) frame$V2 <- 2 frame$V3 <- ...

2

Once you have slogged through all the relatively useless theoretical literature, this paper is a rediscovery (and pretty good write-up) of how basket option pricing is really done in serious quant packages at the big banks.

2

Is it possible to replicate the option of a custom index? Yes and you can find OTC market-makers who will make a price. They use portfolio replication to mimic the payoff of the option with a position in the underlying (Black-Scholes, '73). Even though the underlying custom index is not traded it can be perfectly constructed via its traded constituents. So ...

2

CBOE has something with limited capacity. Yahoo Finance also gives the current option chain. But historical option data is not free. The most affordable I saw is here. I don't know about its validity but their structure seems good and almost clean. More importantly, data seems reliable. p.s. I am not sure if providing the paid data link is within T&C ...

2

Perhaps this paper by Hyun Woo Byun and coauthors is what you're looking for: Using a Principal Component Analysis to develop Multi-Currency Trading algorithms in the FX market They apply principal component analysis to a currency basket of 9 pairs with a 2 month rolling window. In a second step, various techniques (logistic regression, decision trees, ...

2

Freddy has already answered it and my answer had an assumption in it so clarifying - If payoff of basket with underlined securities A,B and C are $$P_b = C_1*P_A + C_2*P_B + C_3*P_C$$ Where $$C_1 , C_2 ,C_3$$ are contants then portfolio delta is $$\delta_b = C_1*\delta_a+C_2*\delta_b+C_3*\delta_c$$ In short as Freddy Said , and I assumed if the ...

2

Please note that this is subjective, but I hope it can help. I was told that Frozen Concentrated Orange Juice forward contracts (FCOJ) are used to have a proxy for weather risk. https://www.theice.com/products/30/FCOJ-A-Futures you can imagine have a look at other agricultural forwards, since for these kind of market, demand is linked to economy level (=...

1

This is not a direct answer to your question as I am not sure whether the instrument you described exists, but OP would probably find the mathematics behind transmission congestion contracts very interesting. Transmission congestion contracts enable the hedging of fluctuations in electricity prices across the power grid, and are auctioned off by regional ...

1

The formula works for total variance, not "strike specific" variance that you need to construct basket vol surface from components, because single historical correlation (or correlation matrix) just does not provide enough information to uniquely reconstruct expected distribution of basket returns (unless for a trivial case where all components are gaussian, ...

1

To develop it from scratch, you could simulate the portfolio of the security combination, and utilize the portfolio's notional value, volatilities into Black Scholes Merton for fair values of ATM options.

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