7,911 reputation
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bio website bachelierfinance.org
location United States
age 45
visits member for 3 years, 5 months
seen 16 hours ago

Worked in a lot of quant areas


Jul
17
comment Arbitrage free implies complete market?
One often thinks of the cost of entering a position as the quantity $q$ times the difference $\nu$ between the offer (bid) and the midpoint. If the spread is $h$ then $\nu=h/2$, so I call it a half-spread.
Jul
1
comment What are the unfair order execution/routing advantages HFT firms apparently have?
It's probably worth adding that off-exchange (dark) pools, of which IEX is one, can make their own rules. IEX is not the only such entity violating price-time. Some dark pools subdivide their traffic into sub-pools according to client type, etc.
Jun
30
comment Self-financing and Black-Scholes-Merton formula
@Hansen unfortunately, as I say, ignoring the LCP is a "practioner thing" so references are rare. For example, I recall Monis doing this up through at least version 8.0, but to find out that fact I had to talk to the quants -- it was not in the documentation. Similarly for various internal investment bank pricing libraries. As to the policy iteration, I first saw a reference somewhere on the Wilmott forums around 2009(?), so you might start there.
Jun
27
comment Self-financing and Black-Scholes-Merton formula
PSOR tends to iterate the underlying Gauss-Siedel solver several times, especially if it hasn't been preconditioned with the "european" solution based on the naive exercise boundary (NEB). Many or most practitioners go to the extreme of completely ignoring the LCP and just applying the NEB, which introduces a fairly tiny error for most payoffs. A more efficient algorithm than PSOR to do this "right" is policy iteration.
Jun
27
comment Self-financing and Black-Scholes-Merton formula
Good document, though as a practical matter PSOR is not a good algorithm to solve the LCP.
May
27
comment Introducing credit risk to an already implemented interest rate model
You've basically already got it, though in most cases one assumes a deterministic term structure of credit spread, rather than making a stochastic model for it.
May
20
comment Create optimal portfolio by Treynor and Jensens Alpha
If you make your metric Sharpe-like, by including a measure of distributional width in the denominator, then there is of course a reward. If that measure is standard deviation, then the mathematics even works out to be nearly identical to Markowitz.
May
13
comment Are Futures exactly Delta One?
Matt's usage of the term <i>forward delta</i> is important here. RRG (and Swab Jat) seem to be forgetting that delta has a denominator. That is to say, when we speak of the delta of a contract, we sometimes need to be explicit about what security that delta refers to (this is particularly obvious for exotics like basket options).
May
12
comment Pricing binary options with kernel density estimation
If you price options off the real-world probabilities like that, you are going to lose your shirt.
May
1
comment Topological methods in finance
Interesting premise: a market metric based on Jones polynomial! I wonder if its behavior differs much from standard correlation metrics. Based on your username, the paper is your own -- it would be polite to mention that in your answer.
Apr
25
comment A question about pricing convertible bond with two different underlying assets
You'll get a better-quality answer if you are more specific about the terms and conditions (T&C) of the bond. In particular, if the holder chooses to convert, is the mixture of assets the conversion happens into determined by the holder, the issuer, or a formula?
Apr
17
comment Usage of Brownian Bridge?
For scrambling, a good place to start would be Hinckernell's Quasi-Monte Carlo methods and their randomizations.
Apr
16
comment American Swaption Pricing with Monte-Carlo method
Use trees or other PDE discretization. Though you say they are "difficult" they are the right approach.
Apr
16
comment American Swaption Pricing with Monte-Carlo method
American exercise is precisely when you want to avoid using Monte Carlo.
Apr
9
comment Are power contracts traded on any stock market?
Power contracts were always the domain of the theoreticians. I never saw one go through our exotics desk (though our software would have supported it, because it was so darn easy to put in the library).
Apr
4
comment Efficient numerical approaches for pricing American Options with multiple sources of noise
I consider Tavella and Randall to be the best place to learn finite difference techniques for finance.
Apr
4
comment How to compare different volatility measures?
You need to define what you mean by best and explain more precisely to get an germane answer.
Apr
4
comment Weighted average implied optionlet/swaptions volatility
Even some traders use weighted averages of surface volatilities as an initial stab at pricing, so you can certainly get in the ballpark that way. The weighting to use would depend heavily on the terms of the contract that needs pricing. For example if it pays off only in low-strike regions you would not necessarily weight ATM vols the highest.
Apr
1
comment How to hedge a derivative that pays the reciprocal of the stock price?
Hint: $\log(1/S_t) = -\log(S_t)$
Mar
30
comment Credit Spread, Transition Matrix
You need a matrix whose square is the annual matrix. The question is covered at quant.stackexchange.com/questions/10645/…