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@bodycamarrestvideos: Officers decide her fate behind the scenes

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Sunday 05 April 2026 02:00:00 GMT
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Can you hedge an option without knowing its volatility? El Karoui, Jeanblanc-Picqué and Shreve show you can, as long as the volatility you use stays above the market's at every instant. Sell a call, price it and delta hedge it at a volatility σ_H while the market realizes σ_t, and your final P&L is ½∫(σ_H² − σ_t²)S_t²Γ_t dt, with gamma computed at σ_H (their eq. 6.7, shown here with zero rates). A call's price is convex, so Γ ≥ 0: if σ_H ≥ σ_t at every instant, no moment can cost you and the hedge covers the payoff on every path (Theorem 6.2), American options included. The cost of that safety is a price above the true one. If σ_H only matches σ_t in total variance, the result depends on timing: you lose when volatility spikes while the stock sits near the strike (Remark 6.3, Appendix B). Limits: continuous prices without jumps, continuous hedging, no transaction costs. σ_H must depend only on time and the stock price (Section 4). The 20/15 and 12/35 numbers are our illustrative example, not the paper's (35 is 34.92%, set so both total variances are exactly equal), and the animations are simulations. El Karoui, N., Jeanblanc-Picqué, M., & Shreve, S. E. (1998). Robustness of the Black and Scholes Formula. Mathematical Finance, 8(2), 93–126. doi.org/10.1111/1467-9965.00047 #finance #quant #trading #algotrading #stocks
Can you hedge an option without knowing its volatility? El Karoui, Jeanblanc-Picqué and Shreve show you can, as long as the volatility you use stays above the market's at every instant. Sell a call, price it and delta hedge it at a volatility σ_H while the market realizes σ_t, and your final P&L is ½∫(σ_H² − σ_t²)S_t²Γ_t dt, with gamma computed at σ_H (their eq. 6.7, shown here with zero rates). A call's price is convex, so Γ ≥ 0: if σ_H ≥ σ_t at every instant, no moment can cost you and the hedge covers the payoff on every path (Theorem 6.2), American options included. The cost of that safety is a price above the true one. If σ_H only matches σ_t in total variance, the result depends on timing: you lose when volatility spikes while the stock sits near the strike (Remark 6.3, Appendix B). Limits: continuous prices without jumps, continuous hedging, no transaction costs. σ_H must depend only on time and the stock price (Section 4). The 20/15 and 12/35 numbers are our illustrative example, not the paper's (35 is 34.92%, set so both total variances are exactly equal), and the animations are simulations. El Karoui, N., Jeanblanc-Picqué, M., & Shreve, S. E. (1998). Robustness of the Black and Scholes Formula. Mathematical Finance, 8(2), 93–126. doi.org/10.1111/1467-9965.00047 #finance #quant #trading #algotrading #stocks


Tập khoẻ thôi brooo #bota20kg #gymtainha #taptatainha
Tập khoẻ thôi brooo #bota20kg #gymtainha #taptatainha
Same aunt same! #fyp #kaspahon
Same aunt same! #fyp #kaspahon


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