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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 ...


7

A popular open-source option for the numerics in .NET is Math.NET (https://github.com/mathnet/mathnet-numerics). It has both managed implementations and allows you to use the optimized MKL native libraries. This use of .NET as a front-end to an optimized native library is quite common. Meta.Numerics (http://www.meta-numerics.net) is an alternative ...


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

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 ...


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

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 ...


4

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 ...


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 think the reason is the following: The bund future refers to the price of a fictituous $10$-year $6\%$ coupon bond. The current ctd bond has a smaller coupon I think ($2\%$ 01/04/2022) - that would account for the price difference right?


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

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

In the derivatives context, "arbitrage free" means almost surely for the probability measure under consideration. This is in opposition with statistical arbitrage used at high frequencies for example. More precisely the assumption is that there is no $T\geq 0$ and self-financed portfolio $V$ such that $V_0 = 0$, $P(V_T < 0) = 0$ and $P(V_T > 0) > ...


3

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 ...


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 ...


3

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 ...


3

Depends on circumstances - if you just trade futures intraday for yourself, secondary market T-bills (http://www.federalreserve.gov/releases/h15/data.htm#fn3) will be good enough.


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

This goes back to the so-called First Fundamental Theorem of Asset Pricing saying that markets are arbitrage free if and only if there exists at least an equivalent risk neutral measure. So the reason why we are using risk neutral measures to price options is because it allows us to represent discounted stock diffusions as martingales and therefore express ...


2

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 ...


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 ...


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

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

This is wrong: effectiveDate / Valuation_date = 10 May 2014 Good that you included the ISIN, which states that the effective date (as contrasted with the issue date) was a few days after 03 May 2013.


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

As I see it the question does not enforce that the market is free of arbitrage. This is why you can get to contradicting prices. Thus you can't actually apply a risk-neutral argument here without making additional assumptions. You yourself provide the example of such an arbitrage. If the underlying process had a B&S dynamics you could just borrow money ...


2

I am too lazy to write up a longer answer and I do not know how to write LateX, so here you go, Pricing Formulas for Binary Range Option


2

This tackles the second part of your question: In a world were interest rates are always zero (for simplicity sake), if the discount price process is a martingale, we have: $E[X_T | F_t] = X_t$ In an arbitrage free world, every price process is a martingale in the risk-neutral measure. Having martingale price processes means that if we build a hedged ...



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