# Tag Info

7

well, it is absolutely in agreement with theory. the correlation as measured by Pearson's coefficient $\rho$ is linear measure in the sense that the bounds [-1,1] are obtained only when transformations of our variables are linear, so if we have variables $X$ and $Y$ then something like $aX+bY+c$ where $a,b\in\mathbb{R^*}$, $c\in\mathbb{R}$ will have ...

5

In simple terms: An ordinary swap might be a 10 year swap of Libor vs a fixed rate; this fixed rate is determined in the marketplace every day and is published by Reuters, Bloomberg etc. as the '10 year swap rate'. Once you enter into the swap this rate remains fixed for you, of course, that is why it is called a fixed rate. But every day Reuters publishes a ...

5

A constant maturity swap (CMS) rate for a given tenor is referenced as a point on the Swap curve. A swap curve itself is a term structure wherein every point on the curve is the effective par swap rate for that tenor. This is analogous to a 3m LIBOR curve represents 3m forward rates for a given tenor. A swap rate can be considered as a weighted-average of ...

5

The main thing to keep in mind with all these different option combination strategies is that you are really trading option greeks! I think the answer to why the calender spread is so popular lies in the special combination of gamma and vega risk: Calendar spreads are the one type of trade where gamma can be negative while vega is positive (and vice versa ...

4

In a vanilla swap, the IR on the floating leg usually depends on the reset period/swap frequency. If frequency is 6m, 6m LIBOR is used for reset, 3m LIBOR for quarterly resets etc. In a floating CMS leg, the rate used is the CMS rate, regardless of the reset frequency e.g: 10yr CMS leg will use the 10 yr CMS rate, regardless of whether the reset happens semi-...

4

If you're reconstructing a payoff as a linear sum of call options, then the procedure is quite simple -> since the payoff of a call is zero up to the strike, and then linear, you start on the left (i.e. most negative value) and move to the right. example 1: long butterfly spread, strikes of 80, 100, 120. start at zero. gradient of payoff is zero: hold no ...

3

If $S_T<K_1$, the payoff is zero, and we have $\frac{(K_2-K_1)S(T)}{K_2} \geq0$ If $K_1 \leq S_T<K_2$, the payoff is $(S_T -K_1)$. We have $$K_1K_2 \geq S_TK_1$$ and $$S_TK_2+K_1K_2 \geq S_TK_2+S_TK_1$$ Thus, $$S_TK_2-S_TK_1 \geq S_TK_2-K_1K_2$$ Finally, $$S_T(K_2-K_1) \geq (S_T-K_1)K_2$$ $$\frac{S_T(K_2-K_1)}{K_2} \geq (S_T-K_1)$$ If $S_T \geq ... 3 The issue is what exchanges recognize as acceptable complex option orders. This is governed by FINRA margin rules like rule 4210 Brokers can only execute orders that are recognized by options exchanges. So what brokers can put on a single order ticket is limited. The most complex spreads defined by FINRA rules would be butterfly spreads, box spreads and ... 3 It depends on the frequency and the horizon. For instance, I got a similar looking chart when I used annual log returns as the input to the log normal distribution and went out 250 years. With daily log returns over a few years, there isn't nearly as much of a decay. However, when you go out 250 years with daily returns you still see the pattern. 3 It depends on the exact structure. E.g., a butterfly can be bought or sold and every market participant understands which individual options are bought or sold given knowledge of the agreed spot level and distance of the wing from spot in regards to agreed strikes. Please note that a butterfly can be structured as a combination of calls but also through ... 2 The best approximation that I know is Li, Deng and Zhou, 2006. It's an analytic approximation where the price is expressed as a direct formula, so easy to implement. If you want to be VERY accurate, here's my paper, J Choi (2018) (Arxiv). It handles the options on any linear combination of assets such as basket and Asian options as well as spread option. ... 2 I've been analysing the same problem and i think that the way to go it's calibrating an interest rate model. Think of it as an option on a bond, there is plenty of literature about that. Also you can look at Quantlib implementation of callable bonds to get an idea of how can it be implemented. 2 ES is supposed to update every 100 msec now in TWS. I imagine the FOPs update slower than that, probably every 300 msec. IB is not a real time feed like others, they aggregate the data and send it on schedule. It's good because it doesn't lag, bad because you don't get every tick. What Matt said is true and good but if you want to stick with Excel you ... 2 There are a few extra things to consider here where you'll get a different answer if you ask a quant or a trader. If we have a european digital that pays \$1 if the underlying is above 120 ($S_0 = 100$) at expiry, then yes i can hedge it with a call spread. This can be approximated with a call spread (with a notional of $\frac{1}{\mathrm{d}K}$, this was ...

2

I think the variance of the instantaneous shifts in the spread is meant: $V \left[ dX \right]=V \left[ dS_1-dS_2 \right]$ And the individual variances (in the conditional and local sense) are: $V \left[ dS_1 \right]= \sigma_1^2 S_1^2dt$ $V \left[ dS_2 \right]= \sigma_2^2 S_2^2dt$ And the covariance term is, assuming the two Brownians are correlated:...

2

Might you be using the tower law in a wrong way? I have the impression you derive your second equation by conditioning by the $\sigma$-algebra generated by $(Y_t)_{t\geq0}$, however note that: $$\mathscr{F}_t\nsubseteq\sigma(Y_t)_{0\leq t\leq T}$$ Hence: $$E\left((X_T-Y_T)_+|\mathscr{F}_t\right)\ \not= \ E\left(E(X_T-Y_T)_+|Y_T)|\mathscr{F}_t\right) \ = \ E(... 2 By selling that additional Put, you're not only collecting the credit, but you're also introducing more risk. In essence, that's the reason the other party pays you for handing them the Put option. I this case, I doubt that you will collect a high premium, if at all, for the 120P expiring in less than two weeks, with the current price at 205. But if the ... 1 Let's say K=1. If c=0.5, you get a shape like this (as you alluded to): And for c=-0.5, you get this shape: So does look like butterfly. 1 Agreeing to your first observation: After orthogonalization, with independent W and W’, and using self explanatory notation for the new diffusion coefficients, which obviously depend on \rho, we can show that, under \mathbb{Q}_Y, we have:$$ dR = R[(\sigma_{XW} - \sigma_{YW})dW + (\sigma_{XW’} - \sigma_{YW’})dW’], $$where R=XY^{-1} (used only Ito ... 1 A single look CMS spread option is simply an option on the difference between the two forward CMS rates and a chosen strike K on a single expiry date t. A CMS spread cap is then a strip of options and pays on each t_i from t_1 to t_n. Both types are quoted by brokers such as Tullet. Both products allow the investor a view on the shape of the yield ... 1 After some testing, it is clear that a value of 0.005 is the most reasonable minimum volatility to use with this model. It is small enough to be a reasonable starting point (extremely unlikely that the real volatility of an option will be lower than this), while still being sufficiently high enough to avoid numerical issues when calculating implied ... 1 Well, the probabilities implied by the market are not equal. If you believe they should be equal, then go ahead and express yourself in the market. The point is , it is not an objective fact that it must be 50/50- that's your subjective opinion. 1 For such problems, you may consider the moment matching approach. For example, you can approximate the combination of terms where the coefficients have the same sign by a log-normal random variable, and then use the approach you mentioned. If all coefficients have the same sign, you can approximate the whole combination by a shifted log-normal random ... 1 BlackRock has the best commercially available prepayment model and Yield Book is basically the industry standard for trading and is decent. 1 prepayment model could be very complicated as there are so many variables could affect the prepayment rates, such as demographic, seasonality, location etc. My experience on this was I knew many companies just directly use some prepayment data from SIFMA instead of building their own model. Typical text bool models are CPR, PSA, SMM. Nowdays, machine ... 1 Your formula, as it stands, is incorrect, at least is if E means the "expected value under real-world probabilities". I wrote a blog post explaining the basic rationale behind risk-neutral pricing where you will see that if the Fundamental Theorem of Asset Pricing theorem holds, you can write: Let X_t=S_{1,t}-S_{2,t}$$e^{-rt} X_t = \mathbb{E}_\mathbb{...

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