# Tag Info

7

I recommend reading Cao, Hansch, and Wang (2004) "The Informational Content of an Open Limit Order Book". They present a simple model for an order-book price called the weighted price ($\mbox{WP}$): $$\mbox{WP}^{n_1 - n_2} = \frac{\sum_{j=n_1}^{n_2} (Q_j^d P_j^d + Q_j^s P_j^s)}{(Q_j^d + Q_j^s)}$$ Where: $n$ is the order book level $Q_j$ is the size at ...

6

You have the right intuition but the approach is not quite right. The issuer has the right to call back the bond at a pre-defined call price. So your decision criterion is "call when the value of the bond >= contractual call price". We are comparing prices in the decision rule, not the YTM of the callable bond with the coupon of the bond. Note that ...

5

Numerical methods are only approximations. So binomial trees, Monte Carlo simulations, and finite difference methods should all produce different numbers. As for whether you should install it for your customers, that can only be answered by what you think your customers want. Do retail customers really want the potential confusion? Are they going to ...

5

Not really a quant question, but a quick search led to this from the CME: http://www.cmegroup.com/market-data/files/CME_Group_Settlement_Procedures.pdf. Unfortunately it depends on the contract, for example: Equity Futures: For S&P and NASDAQ, the settlement price of the lead* month contract is the midpoint of the closing range determined based on pit ...

5

You might want to read this: Size, Value, and Momentum in International Stock Returns by Fama and French (2011) Abstract: In the four regions (North America, Europe, Japan, and Asia Pacific) we examine, there are value premiums in average stock returns that, except for Japan, decrease with size. Except for Japan, there is return momentum ...

4

Generally, there are few or no zero-coupon instruments traded in the market, especially for longer maturities. However, pricing of many derivatives relies on having a zero curve, so it becomes necessary to construct one using available instruments. Aside from derivatives, one can use a zero curve fitted to liquid bonds to price new or less liquid issues.

4

There are two different issues at play here. One is that, of course, you want only the future cash flows to enter the calculation. This is taken care when you set the evaluation date to 6 months from today. In C++, you would say Settings::instance().evaluationDate() = today + 6*Months; I don't remember the corresponding function in QuantLibXL, but you ...

4

A swap does not require a model because its price can be derived from the yield curve without any assumptions about how the yield curve may move in the future. The PFE however is an indication of by how much the swap's mark-to-market may move between now and a moment in the future. It is of course influenced by how volatile rates are. The more volatile ...

4

I have honestly not come across a good book (or good enough review to make me buy the book) on Fund Transfer Pricing. While it is not my career focus, I had to familiarize myself a bit with the topic because of certain requirements involving funding trading operations and the performance of funding specific operations. Personally I would recommend the ...

4

CMS adjustments in single curve context can be roughly explained if you consider a CMS swaplet by the fact that there is a single payment at the CMS rate at a single date and not on the whole strip of the underlying CMS tenor schedule. So if you are trying to hedge a CMS swaplet with the corresponding swap of CMS tenor length (with correct naïve nominal ...

3

You have to look at the terms and conditions on your individual bond. The way the specifications usually work is that a call will result in accrued interest being paid, effectively making up for the lost coupon. Sometimes there's even an extra penalty. A put will result in a loss of coupon in almost all cases, and so is almost always done just after a ...

3

I have a little more informations, so let me share it with you. Even though I think that the frameworks I presented in my question are both corrects (i.e. aribtrage free), it happens to be the case that the market seems to have more "structure". Here is a methodology that allows to retreive market quotes and which is the same as BBG (which is the best ...

3

You should use the full yield curve, discounting cash flows at specific dates using the appropriate zero-coupon interest rate. As to which yield curve, that is often a matter of convention. Generally one uses the LIBOR/swaps curve for all but the most liquid products (in which case you use the treasury curve). The curve is constructed from LIBOR/Eurodollar ...

3

You assume that interest rates are never negative, however, all kinds of strange things happened already in the recent years, e.g. the Euroswiss futures traded above 100 in August 2011, SARON is negative (http://www.six-swiss-exchange.com/indices/swiss_reference_rates/reference_rates_en.html), German short term debt (Schatz) traded with negative yields this ...

2

Assume you have an USD-EUR Cross Currency Swap (3M-FloatUSD+SpreadUSD vs 3M-FloatEUR+SpreadEUR) (spread on USD side is usually zero), collateralized by USD-OIS (Fed Fund) I assume you know the USD-OIS discount curve, then you know the discount curve for USD cash flows. I further assume that you know the USD-3M forwards collateralized w.r.t. USD-OIS (from ...

2

Let's approximate the time to maturity to be 3 years and 10 months. Assume that coupon is paid on March 6 each year. Let face value $F=100$ and coupon $c=0.07375F$. Let the discount factor be $d(0,T)=e^{−r T}$ where $r=0.06535$. The price of the bond is $$ce^{−10/12 \bullet r}+ce^{−22/12 \bullet r}+ce^{−34/12 \bullet r}+(F+c)e^{−46/12 \bullet r}=103.24 \; ... 2 I would say Start with Black Scholes to look at accuracy. In particular, you have a closed formula and you know what the characteristic function for lognormal is. Running FFT and comparing FFT pricing with the closed formula will give you an idea of what are the convergence issues, what is the behaviour at the boundaries (extreme strikes) etcetera. Then ... 2 The question should not be about the swaption pricing formula, its well established and widely accepted and utilized every single day. The question you SHOULD be asking, however, is which underlying volatility model you are using. Its idential to you questioning the use of B-S in transforming vols -> prices, and prices -> vols in the equity world while you ... 2 In my mind you are simply right: you arrive at$$ f(t,S) = S(t) - K e^{-r(T-t)}. $$Assume that t=0, so we are at the inception of the contract, then$$ f(0,S) = S(0) - Ke^{-r T}.  If you choose $K = S(0) e^{r T}$ then the contract value at inception is zero. This simply means that the fair price for the forward is given by $K= S(0) e^{r T}$ which is ...

2

In the following paper: "On the Cross-Section of Expected Stock Returns: Fama-French Ten Years Later" (by Chou, Chou, and Wang), the authors found, using the Fama-Mac Beth two-pass regression, that the size effect becomes insignificant during the post-1981 period, and the Book/Market effect becomes insignificant during the post-1990 period. It is important ...

1

Yea, I just started work at a fixed income shop. We accrete the value of zero coupon bonds based on the coupon rate the bond would have paid if it were an interest/bullet bond. The value of the coupon/accreted rate in the Official statement/indenture of the bond is obviously not the rate the market is pricing the bonds at but it fluctuates around it, ...

1

The problem is to find the best functional form of the utility function plus estimate its parameters. A good starting point is the following draft chapter from an upcoming book which gives a good intuition and many examples: Preferences by Andrew Ang

1

I don't know what is supported by MatLab (I use Java to do such stuff :-). But in case you do not find a solution from the swapbyzero function you mentioned I can suggest a workaround: Value a swap with the annual fix frequence. Given that it is a payer swap (pays the fixed leg), correct the value by: Substract the value of an annual fix coupon bond ...

1

I think Hull treats dilution in his book, and it's extensible to this case. For what it's worth, the strike is typically set low enough that there's little doubt about exercise, meaning there's not much point in modeling the optionality. Most people concentrate on the dilution alone -- particularly the question of the change in fully diluted versus ...

1

In your scenario, the main factor behind the spread would be the forward repo rate implied by the term repo rates on the ctd, one termed to the delivery date of the front contract, the other termed to the back contract. In the current rate environment this will have little to do with the term structure of mm rates. Instead, any difference between the repos ...

1

I don't know if I understand your question correctly but the procedure how to calculate ATM option prices with publicly available implied volatility indices (like VXO) for the vol parameter can be found in the mentioned paper on pages 5-7: How Students Can Backtest Madoﬀ’s Claims by Michael J. Stutzer (2009)

1

This is public knowledge what you need is a good book on how option strategies are built and used... Heres some good starting points/books in which you can get a good framework to start building and applying your FFT option pricing method of choice The volatility surface Options futures and other Derivatives Options Volatility and Pricing

1

Here's an answer from a purely statistical point of view: http://www.duke.edu/~rnau/regnotes.htm#constant And another from Cross Validated: http://stats.stackexchange.com/questions/7948/when-is-it-ok-to-remove-the-intercept-in-lm The lean in both cases is to include the intercept unless there is a strong theoretical reason. A more satisfying answer would ...

1

Time-series regression is not a great method for determining betas on individual securities. Rather, the most common method used by the commercial risk model providers is called "predicted beta" or "fundamental beta." The leader in this area is Barra. The way they define the predicted beta, it appears that they include the constant in the regression.

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