Recent Questions - Quantitative Finance Stack Exchange

I know that the risk-neutral price of a call option with strike price $K$ is given by: $$C(K,S_T) = e^{-rT}\int_{0}^{\infty }(S_T-K)^+g(S_T)dS_t$$ Since a payoff is only valid when $ S_T >K $ this turns into: $$C(K,S_T) = e^{-rT}\int_{K}^{\infty }(S_T-K)\times g(S_T)dS_t$$ Now I wanted to differentiate the call formula once and twice with respect to K, so $\frac{\partial C}{\partial K}$ and $…

Background I am trying to calculate the returns on a sequence of trades performed by an entity, where I do not know the starting capital. Therefore I assume a starting capital of zero. From these returns I want to calculate the Sharpe ratio of a portfolio on which these trades are performed. The initial idea of simply comparing successive portfolio values to calculate returns falls apart in this …

The intrinsic value of a call option is found by subtracting the discounted strike price from the current share price: $IV = S - X/e^{rT}$ Put-Call parity: $S + p = c + X/e^{rT}$ $c = p + (S - X/e^{rT})$ Since the second term is literally the definition of the intrinsic value of a call, should the time value of the call option $(c-IV)$ be equal to the value of a put with the same strike price??? …

I am conducting a comparative analysis of two investment strategies using Monte Carlo simulations: periodic profit-taking and holding the investment until maturity. Specifically, I am simulating price paths for a cryptocurrency (Polkadot) over a 90-day period with 1,000 iterations. The initial parameters are as follows: Initial price: $4.1 Final price: $5.8 Initial investment: $15,000 Days: 90 Nu…

I am trying to test Hurst exponent in different time lag range. However, i got negative values in some time lag range which is weird, because the Hurst exponent should have values within the range from 0 to 1. This is the Python code to calculate the Hurst exponent: *calculate Hurst* lag1 = 2 lags = range(lag1, 20) tau = [sqrt(std(subtract(ts[lag:], ts[:-lag]))) for lag in lags] plot(log(lags),…

Is it possible to construct a central bank meeting date curve, using futures prices & OIS rates, in QuantLib? Specifically, I mean a yield curve with flat (constant) forward rates in between meeting dates, and discontinuous moves on meeting dates (or 1 day after I guess, given that typically the rate change applies the next day). If so, how?

I am looking for long time historical intraday day data on the S&P500 composite for a time horizon like 10 years with a - for example 10-minutes tick - or prices for call/put options on the S&P500 index itself. I checked Bloomberg Terminal and also contacted their Help Desk. They do have intraday data, but they only offer 140 days to export to Excel and 240 days to view in terminal. I also check…

What are the sources one can search for or view / download research articles and other publications on quantitative finance in addition to the Internet search engines?

I'm just starting to read about Arbitrage Trading and am currently looking at zero coupon rates as it's in the textbook I am using and had a question about bootstrapping. Say that I have the maturities and and coupon rates for a 1-year bond, a 2-year bond, and a 3-year bond. In constructing the 1-year zero rate, I can just use the 1-year bond, and in constructing the 2-year zero rate, I use the 1…

I am implementing the layer-by-layer calibration of the time-dependent SABR model described in Hagan, Lesniewski and Woodward, Managing Vol Surfaces . In particular, I am using the effective-parameter formulas around equations (3.7)–(3.8) and the piecewise-constant integral update formulas in equation (3.11) of the paper. For each expiry $T_j$ , I first calibrate a standard SABR smile and obtain …

I always find myself in the unknown charted territory when it comes to non-Linear Instruments. I come across the scenario, How to value the option using Delta Vol surface? Example I have CME traded Soybean option(900 strikes, Underlying traded future (spot) trading at 880 USD-cents/BU) with dec maturity and delta surface from the Bloomberg. a) I need to plug out implied volatility from the del…

Does QuantLib have any helper functions to help with interpolating a non-rectangular strike-expiry option chains into rectangular shapes, such that classes like BlackVarianceSurface can be used?

If you could give one piece of advice to a discretionary trader trying to become more systematic, what would it be? If anyone could help I’d appreciate that.

If you could give one piece of advice to a discretionary trader trying to become more systematic, what would it be? If anyone could help I’d appreciate that.

How do I produce a discount curve to discount AUD cashflows collateralised with USD cash? I have the following data available from Bloomberg: AUD OIS up to 9m AUD 3 month bank bill (3mBB) swaps from 1y - 3y AUD 3mBB/AUD OIS basis swaps from 1y - 30y AUD 6mBB swaps from 4y - 30y AUD 6mBB/AUD 3mBB basis swaps from 4y - 30y XCCY basis quoted AUD 3mBB vs SOFR from 3m - 30y Bloomberg build the AUD OIS…

I am currently developping/finalizing a multi-platform quantitative trading dashboard designed for real-time performance monitoring and risk management across MetaTrader, Interactive Brokers (TWS), and NinjaTrader. The system aggregates live trading data and computes: Real-time and rolling Sharpe ratio Dynamic risk/reward and expectancy metrics Risk of ruin estimation based on live equity curves …

I want to price FX TARFs using the Quantlib library in Python. I want to generate paths using the ql.HestonSLVMCModel vol surface. Then, I want to compare the result to Bloomberg and see if the results are in line. In Bloomberg I can retrieve the SLV parameters clearly: per tenor I can find correlation, vol of vol and mixing fraction. Is it possible in Quantlib to also retrieve it from the SLV m…

I am trying to generate a ql.HestonSLVMCModel vol surface for FX (to generate paths and price TARFs). To start with I need a local vol surface. In FX, strikes are not fixed but quoted in delta. This complicates the use of ql.BlackVarianceSurface because it requires a rectangular grid of vols. In a post by StackG I found a proposed method ( in the comment of user35980 ) whereby the original vols a…

What are some quantitative strategies that can be applied to BTC contract trading or spot trading with decent returns?

These are quite simple models, so forgive me If my question is basic. I am implementing Monte Carlo simulation for European call option pricing under two setups: Constant volatility (GBM with σ = 0.2) Uncertain volatility where σ is sampled from a lognormal distribution per path. The mean is 0.2 and standard deviation 0.05. In theory, I expected the uncertain volatility case to produce a higher o…