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5591Implied Vol From Marketed Move 1A desk says the options market is pricing about a 4.8 point one-sigma move for a stock currently at 100 over the next 20 trading days. What annualized implied volatility does that correspond to?数理金融简单数值题未尝试面试订阅5594Implied Vol From Marketed Move 4A desk says the options market is pricing about a 6 point one-sigma move for a stock currently at 72 over the next 30 trading days. What annualized implied volatility does that correspond to?数理金融简单数值题未尝试面试订阅5596Realized Versus Implied Vol 1A short event window has daily returns [0.012, -0.008, 0.015, -0.004, 0.011]. Using realized volatility = sqrt(252 × average(r 2)), what annualized realized volatility do you get? If the options market had implied volatility 0.24, which side had the better volatility bet ex post?数理金融中等数值题未尝试面试订阅5597Realized Versus Implied Vol 2A short event window has daily returns [0.02, -0.014, 0.009, 0.006, -0.012]. Using realized volatility = sqrt(252 × average(r 2)), what annualized realized volatility do you get? If the options market had implied volatility 0.35, which side had the better volatility bet ex post?数理金融中等数值题未尝试面试订阅5601Event Straddle Outcome 1An at-the-money earnings straddle costs 6 when the stock is at 100. Ignore discounting and any post-event vol mark effects, and suppose the stock moves by 8.5 in absolute terms by expiry. What are the buyer and seller PnL per share, and who did better?数理金融中等数值题未尝试面试订阅5602Event Straddle Outcome 2An at-the-money earnings straddle costs 2.4 when the stock is at 52. Ignore discounting and any post-event vol mark effects, and suppose the stock moves by 1.7 in absolute terms by expiry. What are the buyer and seller PnL per share, and who did better?数理金融中等数值题未尝试面试订阅5604Event Straddle Outcome 4An at-the-money earnings straddle costs 4.5 when the stock is at 75. Ignore discounting and any post-event vol mark effects, and suppose the stock moves by 3 in absolute terms by expiry. What are the buyer and seller PnL per share, and who did better?数理金融中等数值题未尝试面试订阅5606Variance Risk Premium Arithmetic 1A simplified volatility contract settles on annualized variance difference notional × (implied vol 2 - realized vol 2). If implied volatility was 0.26 and realized volatility turned out to be 0.19, what is the signed variance gap and the contract PnL on notional 2,000,000? Which side benefits?数理金融困难数值题未尝试面试订阅5611Why Implied Can Exceed RealizedWhy can implied volatility systematically trade above subsequently realized volatility even in a fairly efficient market?数理金融中等essay未尝试面试订阅5612Why Realized Vol Is Path DependentWhy can two stocks with the same start and end price over a week have very different realized volatility?数理金融中等essay未尝试面试订阅5613Why Event Vol Collapses After The PrintWhy do near-dated options often lose a large amount of implied volatility immediately after earnings, even if the stock barely moves afterward?数理金融中等essay未尝试面试订阅5614Why A Directional Winner Can Still Lose On VolHow can an option buyer be directionally right on the stock yet still lose money because implied exceeded realized?数理金融中等essay未尝试面试订阅5615Why Selling Rich Vol Is Not Free MoneyIf implied volatility is usually above realized, why is systematically shorting options still risky?数理金融中等essay未尝试面试订阅5867Daily Break-Even Move From Implied VolA stock trades at 80 with 32% annualized implied volatility. To roughly the nearest cent, what one-day one-sigma move (in price points) does that implied volatility price in, using 252 trading days?数理金融简单数值题未尝试免费5868Theta Versus Gamma On A Hedged DayYou are long a delta-hedged option with gamma 0.04 on a stock at 100, priced at 20% implied vol. Over one trading day (1/252 year) the stock moves 1.5 points. Using gamma P&L = 0.5·gamma·(dS) 2 and theta P&L = -0.5·gamma·S 2·sigma impl 2·dt, what is the net P&L for the day, to four decimals?数理金融中等数值题未尝试免费5869Hedged P&L From The Variance GapApproximate the total P&L of a long delta-hedged option by 0.5·gamma·S 2·(sigma real 2 - sigma impl 2)·T. With gamma 0.05, S = 50, realized vol 0.30, implied vol 0.22, and T = 20/252 years, what is the approximate P&L, to four decimals?数理金融困难数值题未尝试面试订阅5870How Many Daily Moves To Break EvenA stock at 100 has 25% annualized implied vol, so its one-day one-sigma move is about 1.5749 points. An at-the-money straddle costs 5 points. Treating break-even as the cumulative absolute move equalling the premium, how many one-day one-sigma moves does the premium correspond to, to four decimals?数理金融中等数值题未尝试免费5871Vega P&L From A Vol RepricingYour position has total vega of 20 dollars per one full volatility point (i.e. per 1.00 change in sigma). Overnight the implied vol used to mark the book rises from 22% to 27% with spot unchanged. Ignoring all other Greeks, what is the mark-to-market vega P&L in dollars, to two decimals?数理金融简单数值题未尝试免费5872Realized Vol From A Six-Day PathOver six days the daily returns were [0.010, -0.015, 0.022, -0.006, 0.013, -0.009]. Using realized vol = sqrt(252 × average(r 2)), what annualized realized volatility results (four decimals), and was it above or below a quoted 20% implied?数理金融中等数值题未尝试免费5873Straddle Premium Versus Expected MoveA stock at 120 has 28% annualized implied vol over the next 30 trading days. Under a lognormal-approximated normal model, the expected absolute move is S·sigma·sqrt(T)·sqrt(2/pi). What is that expected absolute move, to four decimals (T = 30/252)?数理金融中等数值题未尝试免费