Chris Taylor
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What mathematical theory is required for high frequency trading?
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26 votes

Hah! There is no such thing as the “rigorous mathematical underpinning” of high frequency trading - because HFT, like all trading, is not primarily a mathematical endeavour. It’s true that many ...

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Shape and geometry of the yield curve
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24 votes

You can't make any concrete statements about the monotonicity, convexity or even sign of the yield curve. Yields are almost always positive, and in the past (2007 and earlier) you could find people ...

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Trading interview gambling question
16 votes

An alternative approach is to size your bet to maximize your expected utility, which is assumed to be given by a function $u(w)$ of your total wealth $w$. This could be a better approach than using ...

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American Options relation between greeks
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16 votes

No, you should not expect such a relationship to hold in general. The reason is that American options have an "exercise barrier" which European options don't, and this results in different prices and ...

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What is the difference between pull to par and roll down in both mathematics and conceptual?
14 votes

Pull-to-par just says that a bond's (clean) price will converge towards its face value as the bonds approaches maturity. There is nothing really interesting about pull-to-par - a bond's (clean) price ...

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Is short-gamma inherently a losing strategy?
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11 votes

You can't lose more than you invested by writing covered puts, because you keep enough cash to cover any potential losses from the puts. That's not to say that your losses can't be substantial, of ...

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Reliability of CDS indices?
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11 votes

The indices have different quoting conventions. The way that a CDS index is traded is that you pay a fixed amount per year for protection in case of default (100 bps for IG, 500 bps for HY) and ...

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Would it be possible to combine long butterfly with long straddle, achieving profit no matter the outcome?
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10 votes

Your butterfly is short a straddle and long a strangle. If you add a long straddle with the same strike/notional you are now just long a strangle. The payoff for a strangle is zero if the terminal ...

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What is the appropriate benchmark for a Long/Short VIX futures strategy?
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9 votes

If your strategy truly has no directional bias, then the benchmark should be cash (ie whatever you would earn using the capital in your trading account and taking no risk).

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Price of bond future, given a specific interest rate?
9 votes

Treasury bond futures are surprisingly complicated - this is an attempt at a short explanation, it will obviously gloss over some details, but hopefully gives you a flavour of how they are priced. ...

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Do price approximations lead to arbitrage opportunities?
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8 votes

No. The dirty price is the market's estimate of fair value for the bond. The clean price is just a quoting convention (so that the price doesn't jump when you pass over a coupon date). The market ...

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How much capital to allocate between two trading strategies given average daily P&L and their Sharpe Ratios?
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8 votes

To be consistent with the average daily returns that you specified, your first strategy would need to have a daily standard deviation of 31,749 USD and the second a standard deviation of 7,937 USD. ...

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Vol, Gamma, Vega -- essentially all the same?
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7 votes

They are not the same, but they are related. Gamma is sensitivity to realized volatility. Vega is sensitivity to implied volatility. Vanilla options are always long gamma and long vega, so they are &...

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ICE futures settlement prices change with zero volume and zero OI
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7 votes

These contracts follow standard ICE procedures for calculating settlement prices, which can be found in section 2.4.6 of this document. A high-level overview of the procedure is -- An 'anchor' expiry ...

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Predict the behavior of a time series (P&L trading desk)
7 votes

Without seeing your trading desk's P&L it's impossible to say whether it is predictable or not. But here are a few thoughts - There's no reason to think that it isn't predictable. In general, ...

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Drift rate vs. Riskless rate in the Black-Scholes model
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7 votes

Let's take your questions in turn - If volatility isn't a concern, an investor is concerned with $$ E[\log S_T] = \log S_0 + (\mu - \tfrac{1}{2}\sigma^2)T $$ when deciding to purchase a stock, ...

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How do I get a good mid-price?
7 votes

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 ...

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How to prove Gamma is the same for a European call and European put with the same inputs?
6 votes

Put-call parity says that a call and put (worth $C$ and $P$ respectively) with the same strike $K$ have the following relationship with the spot rate $S$, risk-free rate $r$, and time to maturity $T$ -...

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Face Value of SOFR futures
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6 votes

The 3M futures are worth \$2500 per index point and the 1M futures are worth \$4167 per index point. The index is $$P = 100 - R$$ where R is the compounded SOFR (annualized) over the reference ...

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Is being a quant as easy to look for high paid jobs as before
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6 votes

The kind of jobs a quant would do has changed a lot since the crisis. I wouldn’t say there is more or less demand for quants, just that there is demand for them to do different things. For example, ...

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Estimating the historical drift and volatility
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6 votes

By looking at log returns, you are examing the stochastic process $$ Q_t = \log S_t $$ given by $$ \begin{align} dQ_t & = \left( \mu - \tfrac{1}{2}\sigma^2\right) dt + \sigma\, dB_t \\ & \...

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How to calculate the daily carry on a bond future?
6 votes

There are three sources of carry for bond futures - Carry on the underlying (coupon accrual and yield roll-down) for which you just compute the carry on the cheapest-to-deliver as you suggest. ...

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What causes poor returns in pair trading of very cointegrated securities?
6 votes

A few possibilities - Trading costs kill your returns (often a problem for very highly correlated securities) Mean reversion of the cointegration spread is either very weak, or happens over periods ...

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What are flickering orders?
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6 votes

A "flickering" order is one which is repeatedly submitted and cancelled (whether it's at the top of book or not). The answer from @chollida mentions that "the goal typically is to either slow down ...

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Is there a way to tell if a time series price data is reversed?
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5 votes

This is a great question! The simple, boring answer is clearly "no" - given a time series of stock prices, there is no way to tell for certain whether the price series has been reversed or not. For ...

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For which would you expect the liquidity on instrument X to be the greatest: its spot, future, option or swap?
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5 votes

Completely depends on the asset class. For currencies (including GBP/USD) the spot market is an order of magnitude more liquid than forwards, futures or options. However, some currencies with trading ...

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Relation between ATM, RR and BF
5 votes

The ATM is an outright position (long 50 delta put and 50 delta call) so the main exposure is vega. It is the riskiest of the three, and demands a higher bid-offer spread from market makers to ...

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Difference between FRA and a zero coupon swap
5 votes

A forward rate agreement is an agreement to exchange a fixed for a floating rate over one period, with the payment being made at the start of the period. A zero coupon swap (with both legs paid at ...

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Is forex trade set up where profit target is twice as far from stop loss is good strategy?
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5 votes

If you have no edge, then you would indeed expect twice as many losing trades as winning trades, so you would net out to zero return on average (negative after commissions and trading frictions). This ...

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Theoretical models for options bid-ask spread?
Accepted answer
5 votes

When trading options it is most useful to think in terms of implied volatilities, rather than option prices. For vanilla options, there is a one-to-one relationship between implied volatility and ...

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