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18

Here is a short list (to be edited and improved - community wiki) : Standard brownian motion (also called Wiener process) for which: $d\, W_t \sim \mathcal N(0, \sqrt{d t})$ Geometric brownian motion, used in the Black-Scholes model (1973): $d\,X_t = \mu X_t\,dt + \sigma X_t\,dW_t$ Constant elasticity of variance ("CEV") model (1975): $d\,X_t=\mu X_t dt + \...


12

There was a proxy called the ECU. You should be able to use the weights on the Wikipedia page to get a time series back to 1979. Alternatively, the St. Louis FRED also provides this time series.


12

The majority of the movement in currencies is in the spot rates, rather than in the term structure. A 3-month rolling hedge would always be protecting against movements in the spot rates, no matter when they happen. Using your example, if the current EUR/USD rate is 1.3333, you might be able to get a 3-month forward at 1.3339. (Forgive me if I have the ...


11

You kind of answered the question yourself. Precisely because different market participants use different inputs to their pricing models, it is much easier to quote one single input (implied vols) than the output of 5 different inputs (BS option price). What is important is that you clearly differentiate between quoting and agreeing on the trade vs. the ...


10

Implied volatility is the volatility implied by some model. You will have a skew if your model is implying different volatilities for different strikes. However, the realized volatility of the underlying will be the same for all strikes. So, when you are dealing with realized vol, you can drop the "moneyness" axis. Volatility cones can help you compare ...


9

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] + coef(...


9

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 ...


9

The first column is just a unique id tagged by Gain; this allows you to separate multiple messages that come in with the same timestamp. D means "dealable": this means that a trade could take place. According to this thread, Gain is known for not dealing around events like major news announcements. [Note: In EBS data, which is much more reliable, "D" ...


9

The fx market, contrary to most other asset classes is an almost entirely fragmented over-the-counter market, aside the very small number of fx futures that are trading at dismal liquidity levels. Therefore, you will not encounter a single serious liquidity provider that will take a stab at estimating total traded volume in any of the currency pairs. Having ...


7

For starters, I am not even sure why you need to ask this question. There is literally years of free tick data available for FX, just check out quant.SE's data wiki. Having said that, a Gaussian is a very poor fit to high-frequency data, particularly FX. Your strategy for simulating data depends on the idea behind the simulation. If you wish to actually ...


7

Unless explicitly mentioned, iShares ETFs do not apply any currency hedging directly. (See the factsheet for the case of IJPN. The base currency is USD merely because it is the common currency for a set of identical funds offered in many different versions around the world. At the end of each day they mark their books in USD, converting their JPY-...


7

I work extensively with currency models and have to admit there is not much in the public domain regarding recent published research that may satisfy your needs. Some of the below mentioned models incorporate stochastic components but please keep in mind that most research on currencies focuses on fundamentals (such as balance of payments) and depending on ...


7

The formula $F^X(t,T) = E_t^d\left(X_T \right)$, under the domestic risk-neutral measure, is problematic. Note that, at time $t$, the forward exchange rate $F^X(t,T)$, for maturity $T$, is the exchange rate such that the payoff $X_T-F^X(t,T)$ has a zero value at $t$. That is, \begin{align*} B_t^d E_d\left(\frac{X_T-F^X(t,T)}{B_T^d} \mid \mathcal{F}_t\right)=...


7

Ask minus bid has nothing to do with the mid price - it is the spread. Generally you see a collection of bid/offer orders resting on different price levels. In the simplest case, you just see one bid at price $p_b$ and one offer at price $p_a$. In this case the mid price is $$ p_m = \frac{p_a + p_b}{2} $$ That's all there is to it - you don't need to "...


7

An FX Swap can be described as "borrowing in one currency and lending in another". When put this way it is clear that it has something to do with interest rates in the two currencies. You will be very happy if the i.r. in the currency borrowed rises and the i.r. in the currency lent falls the day after you do the deal, because you will have locked in more ...


7

Be careful of your rate conventions! The issue here is that all your rates are expected to be in units of domestic vs 1 unit of foreign. So for example USDCAD is 1.3347, you really need to be using 1/1.3347 = 0.749 USD per 1 CAD. So, your inputs need to be $$ \begin{align} S &= 1 / 1.3347 \\ X &= 1 / 1.3338 \\ R_d &= 0.75\% \\ R_f &= 0.50\% ...


7

Yahoo has changed their site structure. The new download URLs look like this: https://query1.finance.yahoo.com/v7/finance/download/MSFT?period1=1463461200&period2=1494910800&interval=1d&events=history&crumb=lHxk.yfuuzZ These links originate from pages like this: https://finance.yahoo.com/quote/MSFT/history?period1=1463461200&period2=...


6

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 ...


6

The time to expiry is required, but it's included in the inputs: the two discounts $e^{-rT}$ and $e^{-qT}$ and the standard deviation $\sigma\sqrt{T}$. You might argue it could be documented more clearly, and I might agree with you.


6

Today (1 day after the fact) the following headline appeared in the Financial Times: "September Fed rate lift-off put in doubt, Fallout from China’s currency move turns market mood". If true, this would certainly explain why the USD declined (i.e. the interest rate rise that everyone expected has been postponed). However, in my experience it is very hard to ...


6

What happened was totally unexpected end of peg against the euro @ 1.2CHF regime that Swiss central bank aborted. See some articles about it. As far as I know nobody in the markets knew, there was no indication whatsoever.. In terms of management, I'm afraid lots of people got heavy losses, particularly banks (Austria, Poland, Hungary) - lots of Swiss loans ...


6

The top chart is called a 'candle stick chart' or 'OHLC candlestick' or 'OHLC bar chart' http://multicharts.com/trading-charts When the price goes down during a time interval (from O to C) the box is filled in orange, when the price goes up it is green bordered with black inside. The exact colors are a matter of taste, as long as they are clearly different ...


6

Dukascopy offers historical tick data. Through their historical data website you can download what you want, but registration is required, and lots of manual clicking. However if you are comfortable with scripting, you can directly download the tick data yourself. The URL pattern is http://www.dukascopy.com/datafeed/{currency}/{year}/{month}/{day}/{hour}...


6

$$F = Spot \times e^{(\text{local interest rate} - \text{foreign interest rate}) \times T}$$ where $Spot$ = AUD per dollars. $T$ is the time to maturity of the contract (in years). So for example if the contract expires in 1 year and a half, $T = 18/12 = 1.5$.


5

I am not sure why your question had so many upvotes because in currency markets anything else but triangular arbitrage does not exist. What is a quadrangular arb, I have never heard of it despite having traded fx among other asset classes for over ten years now. Think about it: Lets say you observe the price of EUR/USD. You can build triangular arbs by ...


5

Maybe not really an answer, but a justification of your approach. It's likely that your results can be expresses as $$ \mathsf EX_1 = 1.2\text{ and }\mathsf EX_2 = 2 $$ where $X_i$ for $i=1,2$ is a random pf of a situation in a class $i$ (we denote it $S_i$). Your method solves the following problem: given a fixed number of trials we would like to ...


5

Looking at the original headers for some recent data we have something like this: lTid cDealable CurrencyPair RateDateTime RateBid RateAsk So D would seem to be "dealable", but to be honest I couldn't find an example of a non-D value in the files (I haven't looked thorougly though), so I don't really get it. The cryptic ID, is a tick identifier,...


5

Fatih Yilmaz, formerly of Bank of America (currently BlueGold), has a piece called "Imaginal Spreads and Pairs Trading" on exactly this topic, if you can find it (I couldn't find a copy on the public internet), originally published April 17, 2009. He writes: Academics and industry practitioners generally concentrate on time series aspects of currency ...


5

Liquidity Since this is an asset class which is so tightly coupled with interest rates - it makes good products for clients inherently complex. It also makes good sense to make wider markets for more exotic products than the plain vanilla ones - in which razor-thin spreads rule (and trading huge notionals is not everyone's cup of tea)


5

It depends on what aspect of ZAR you are trying to take a position on. As A K pointed out, if your book is in USD and you want to take a position on the spot rate itself, then just have a USDZAR position. Yes, it is correlated with EURUSD because of both EUR-ZAR correlations and because of USD variations, but that's part of the USDZAR tradeoff. If, ...


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