GLOBAL SEARCH
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中文题目A European call is priced under Black-Scholes with spot 100, strike 100, rate 0.03, dividend yield 0, maturity 1, and initial volatility 0.2. If volatility changes to 0.25 while all else is unchanged, what are the old and new call prices?
打开 →A European call is priced under Black-Scholes with spot 95, strike 100, rate 0.04, dividend yield 0.01, maturity 0.5, and initial volatility 0.22. If volatility changes to 0.28 while all else is unchanged, what are the old and new call prices?
打开 →A European call is priced under Black-Scholes with spot 120, strike 110, rate 0.02, dividend yield 0, maturity 1.5, and initial volatility 0.18. If volatility changes to 0.24 while all else is unchanged, what are the old and new call prices?
打开 →A desk uses half-spread = base + k*sigma_1s*sqrt(horizon_seconds) + buffer. With base=0.004, sigma_1s=0.08, horizon=4, k=1.1, and buffer=0.002, what half-spread should it quote?
打开 →A desk uses half-spread = base + k*sigma_1s*sqrt(horizon_seconds) + buffer. With base=0.0045, sigma_1s=0.07, horizon=25, k=1, and buffer=0.001, what half-spread should it quote?
打开 →In a GARCH(1,1) model with $\omega=1$, $\alpha=\frac{3}{20}$, and $\beta=\frac{3}{5}$, suppose the current squared return is $r_t^2=4$ and the current conditional variance is $h_t=5$. Compute $h_{t+1}$.
打开 →For a GBM, the ratio of the 95th percentile of S_1 to its median is observed to be 1.9. What volatility sigma does this imply?
打开 →For a GBM, the ratio of the 97.5th percentile of S_1.5 to its median is observed to be 2.2. What volatility sigma does this imply?
打开 →Choose b so that sqrt(1+6x) * exp(bx) has no linear term in its Taylor expansion around 0.
打开 →Current variance is v0 = 0.04, long-run mean is theta = 0.09, mean-reversion speed is kappa = 2, and horizon is T = 0.5. What expected forward variance E[v_T] and annualized volatility sqrt(E[v_T]) does the model imply?
打开 →An equal-weight portfolio holds two assets with volatilities 0.04 and 0.09. The current correlation estimate is -0.2, but stress testing revises it to +0.3. With weights unchanged, what is the new portfolio volatility, and by how many volatility points does it rise versus the ori
打开 →In a Cox-Ross-Rubinstein tree the volatility is σ=0.25 per year and each step is Δt=0.25 years. Using u=e^{σ√Δt} and d=1/u, what is the up factor u (to four decimals)?
打开 →At one maturity bucket, the desk estimates the endpoint instantaneous forward volatility sigma(t,T)=0.015 and the HJM no-arbitrage drift alpha(t,T)=0.027. In the one-factor relation alpha(t,T)=sigma(t,T)*integral_t^T sigma(t,u) du, what value is implied for integral_t^T sigma(t,u
打开 →A GARCH(1,1) model $h_t=\omega+\alpha r_{t-1}^2+\beta h_{t-1}$ has $\omega=0.04$, $\alpha=0.12$, $\beta=0.80$. Here $h_t$ is the conditional variance of daily returns. Report the long-run (unconditional) daily volatility $\sqrt{\bar h}$ as a decimal.
打开 →A desk sets half-spread proportional to expected holding-period volatility: h = c*sigma*sqrt(T). It currently quotes h=0.05 at sigma=0.02 per unit-sqrt-time and T=1. If realized volatility doubles to sigma=0.04 and expected holding time rises to T=4, what half-spread should it qu
打开 →A return $R$ is conditionally Gaussian: \[ R\mid V=\sigma \sim N(0,\sigma^2), \] where $V$ equals $1$ or $2$ with probability $1/2$ each. Compute the characteristic function of $R$ and explain why $R$ is not itself Gaussian.
打开 →A position's expiry profit is large and positive far below a price L, declines linearly to a single flat negative minimum across a middle range, then rises linearly again and becomes large and positive far above a price U>L. No stock is held and the minimum loss is bounded. Name
打开 →In the martingale derivation, why does higher volatility usually help a call even though the discounted expected stock price itself does not change?
打开 →In a one-factor HJM setup with maturity gap tau=T-t=2, the desk observes an instantaneous forward drift alpha(t,T)=0.045 and assumes the volatility is constant across the bucket. Using alpha=sigma^2*tau, what sigma is implied?
打开 →In a one-factor HJM setup with maturity gap tau=T-t=1.5, the desk observes an instantaneous forward drift alpha(t,T)=0.06 and assumes the volatility is constant across the bucket. Using alpha=sigma^2*tau, what sigma is implied?
打开 →A variance swap has observed 30 trading days out of 90. Realized variance so far is 0.035, and the current fair full-life variance strike is 0.038333. If the remaining window is assumed to carry one flat volatility level, what annualized volatility does that imply for the remaini
打开 →Around the volatility strike K_vol, a variance swap with variance notional N_var is often locally matched to a vol swap with vega notional N_vega via N_vega = 2*K_vol*N_var. If N_var=100000 and N_vega=40000, what K_vol is implied?
打开 →Using N_vega = 2*K_vol*N_var, if N_var=75000 and N_vega=27000, what volatility strike K_vol is implied?
打开 →Two strategies have the same estimated edge, but one has much higher realized volatility and fatter drawdowns. Which should be shrunk more aggressively from full Kelly?
打开 →For a GBM, the ratio of the 90th percentile of S_0.5 to its median is observed to be 1.3. What volatility sigma does this imply?
打开 →Why is it not contradictory to use implied volatility for option marking while using a separate physical return forecast for directional views?
打开 →A Monte Carlo estimator has sample standard deviation 5 across n=400 paths. Using the normal approximation, what is the 95% half-width?
打开 →Two strata have population weights N1=0.6 and N2=0.4. Their standard deviations are sigma1=2 and sigma2=unknown. Under equal-cost Neyman allocation, the desk wants stratum 2 to receive 50% of the samples. What sigma2 is implied?
打开 →Using N_vega = 2*K_vol*N_var, if N_var=120000 and N_vega=60000, what K_vol is implied?
打开 →A signal's average daily alpha over 25 days is $0.8$, and the daily standard deviation is known to be $2$. Test $H_0:\mu=0$ against a two-sided alternative at the 5% level using a z-test.
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