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Quantitative methods for financial modeling, derivatives pricing, and risk an...
Passed 14 of 24 test cases with the skill, and 14 of 24 without it.
1 fixed13 passed either way9 still failing1 broke
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A test case the skill fixed. Same model, same prompt, with and without the skill.
In financial risk management, Value at Risk (VaR) is often criticized for ignoring tail severity beyond the threshold. How should Expected Shortfall (Conditional VaR) be computed from a sorted historical return series given the VaR cutoff index?
| Checked | Without skill | With skill |
|---|---|---|
| Computes Expected Shortfall as the negated mean of all return values strictly below the VaR quantile index. | Missed | Passed |
The instructions your model reads when the skill loads.
A rigorous skill for applying quantitative methods to financial research, covering derivatives pricing, portfolio optimization, risk modeling, and time series econometrics. Designed for academic researchers and quantitative analysts.
The foundational model for European option pricing:
import numpy as np
from scipy.stats import norm
def black_scholes(S: float, K: float, T: float, r: float,
sigma: float, option_type: str = 'call') -> dict:
"""
Black-Scholes European option pricing.
Args:
S: Current stock price
K: Strike price
T: Time to maturity (years)
r: Risk-free rate (annualized)
sigma: Volatility (annualized)
option_type: 'call' or 'put'
"""
d1 = (np.log(S / K) + (r + 0.5 * sigma**2) * T) / (sigma * np.sqrt(T))
d2 = d1 - sigma * np.sqrt(T)
if option_type == 'call':
price = S * norm.cdf(d1) - K * np.exp(-r * T) * norm.cdf(d2)
else:
price = K * np.exp(-r * T) * norm.cdf(-d2) - S * norm.cdf(-d1)
greeks = {
'delta': norm.cdf(d1) if option_type == 'call' else norm.cdf(d1) - 1,
'gamma': norm.pdf(d1) / (S * sigma * np.sqrt(T)),
'theta': -(S * norm.pdf(d1) * sigma) / (2 * np.sqrt(T)),
'vega': S * norm.pdf(d1) * np.sqrt(T),
test cases passed, vs 14 / 24 without
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