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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] + ...

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. ...

@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 <- ...

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 ...

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 ...

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.

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 ...