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20

Many of them are on my website at emanuelderman.com. Others I probably have anyway. Feel free to email me


8

I had read some of them; actually, it does not exist an on-line library that collected them (or, better, it existed here, but it seems the website does not work anymore). I reported here below some of them that you did not find: More Than You Ever Wanted To Know* About Volatility Swaps Model Risk The Volatility Smile And Its implied Tree Enhanced ...


6

the problem is that the pay-off has discontinuous first derivative. Try a contract with pay-off that is twice differentiable and it will probably work. The problem is that all the value comes from the tiny number of paths within $\Delta S$ of the strike, and these paths have huge value. This is a well-known problem. As the bump size goes to zero, the ...


2

It depends on how one is thinking about the hedge. One might be thinking of it as A hedge against catastrophic risk (default of the issuer), or A hedge against changes in (market-implied) default intensity or hazard rate In the former case, which seems to be how you are considering it, the hedge is a static hedge, kept for up to 5 years, and insulates ...


2

I am a professor too and I did work with Siemens Corporate Technology which provides the quantitative technology for their copper and electricity trading (Siemens being one of the biggest players in this area in Europe). They are mainly using sophisticated neural networks. We also published a paper together, see my answer here: What types of neural networks ...


2

Most index options are options on futures, so to delta hedge a single option position, you trade the corresponding future. For example, say you sell 10 delta 50 calls on the CME Emini S&P. To delta hedge them, you'd buy 5 CME Emini S&P Futures with the same expiry date as the options. As you say, you could hedge with the basket instead, but for ...


2

Assuming zero interest, the put option has the price \begin{align*} KN(-d_2)-S_0N(-d_1), \end{align*} and delta $-N(-d_1)$. When $N(-d_1)$ units of stocks are shorted and invested in bonds, the total value in bonds is $KN(-d_2)$, which is indeed greater than the option price. However, as you have shorted $N(-d_1)$ units of stocks, your portfolio value is ...


2

If you are investing an amount $M$, split over deals indexed by $i$ and with a weight $w_i$, then your dollar position in each share will be $w_i M$. The exposure to the index will be $\sum \beta_i w_i M$ You should realize that this will not hedge idiosyncratic risks. In general, the more deals you have, the better this type of hedge should work (assuming ...


1

we should first define some notation before discussing pricing. Let $t_0$ be initial time and $ t_1, . . . , t_M$ be pre-specified exercise dates with $t_0 < t_1 < · · · < t_M = T$ , the final maturity, and $Δt = t_m−t_{m−1}$. Without a loss of generality it is assumed exercise dates are equidistant. To price a Bermudan option, its value is split ...


1

I think u can hedge using the description given in JC hull.. here he uses index futures. A detailed explanation is given for one stock. I think u can extend it to a portfolio. Also one can hedge by combining two or three stock indices. See page 33 in this link http://www2.fiu.edu/~dupoyetb/Financial_Risk_Mgt/lectures/Ch03.pdf


1

In a nutshell, the client only manages their own position, with the client credit line provided by the broker, whereas the broker manages all their clients' positions, using the broker credit line with their provider banks. You can work it out from there. Interest is presumably to do with cash deposits and loans.


1

It's a combination of too few sample paths and/or too small an increment. Your estimation error on the price is magnified by the $dS^2$. Try using a larger sample or a larger increment. Alternatively, you can use a multiplier instead of a fixed increment; in my experience, it usually yields better results.


1

You have already agreed to pay $QK$ EUR at $T$ to receive $Q$ units of A. If you sell $Q$ lots of $F^A(t,T)$ then you will receive $Q F^A(t,T)$ EUR and deliver $Q$ units of A. The combined flow is now just in EUR: at $T$ you receive a net of $Q(F^A(t,T)-K)$ EUR. You can hedge that by selling $Q(F^A(t,T)-K)$ of $F^{FX}(t,T).$ Then with both hedges, the net ...


1

That seems to be a nice paper but I haven't worked through it completely yet. As I understand it, the goal is to replicate the holding (by an investor) of an European option using an American option, stock and bonds in a self-financing manner. As the value of the underlying changes this requires rebalancing of the option and the bond, i.e. hedging. Since ...


1

This sounds like quadratic hedging. If you have the return of the assets $r_X$ and $r_Y$ with negative correlation $\rho$ between the two (we could think of bonds and stocks) and more variance in one of them then the problem of weighting the two by $w$ is (assume zero expected returns for ease of presentation) $$ \text{risk} = E[(w r_X + (1-w) r_Y)^2] ...


1

I am not sure I fully understand your question. Options it just derivative contracts (wager) between two parties, there is no ‘real’ assets bought to support the +/- value change the option might have during its duration. When the exercise date is upon the option, and you are the winner, you are paid according to the WAMC of the index – e.g. 3.4% of your ...


1

This is a much simpler problem than stated, (assuming the correlation is positive). In 1 month you need to BUY 2mn of jet fuel. If Jet fuel prices go up, you lose money as it's more expensive. If jet fuel prices go down, you make money as it's cheaper. So to "hedge" your risk you will LONG the heating oil, as you are not in the business of speculating on ...


1

In the Merton jump diffusion model, the stock price process consists of a continuous part and a discrete part (this one represents the jumps). While deriving the PDE for the riskless portfolio and imposing the riskless evolution, the discrete part can't be instantaneously hedged. In fact, you can assume that the effects of jumps can be nullified on average, ...


1

There are two things: First: You have one stock of $B$ (worth \$30) and the calculation tells you to short 1.14 stocks of $A$. Of course you can only short whole stocks. So you would have to decide wether to short 0,1 or 2 stocks. This is a question of contract size, or in this case just size. Second: Usually we speak about hedging in portfolio context. In ...


1

My 10 cents: Yes, the EUR is trading at a discount to USD. Think 100 - 2.8 = 97.2 for EUR, whereas 100 - 1.5 = 98.5 for USD so EUR is at a discount to USD. The calculation of premium and discount is in the forward pips. In your case it's spot - pips = forward 1.3195 - 0.0195 = 1.3000 So yes, the EUR cost in 6 months is $2500 / 1.3 = €1923.07 you agree ...



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