Reconstruction of the Time-Dependent Volatility Function Using the Black–Scholes Model

<div>Construction of volatility by the SPL and proposed algorithms when the exact volatility is (a) <svg height="13.4393pt" id="M178" style="vertical-align:-2.2681pt" version="1.1" viewbox="-0.0498162 -11.1712 66.6839 13.4393" width="66.6839pt" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink"><g transform="matrix(.013,0,0,-0.013,0,0)"><path d="M548 455L523 469C505 448 490 439 461 439C416 439 374 447 316 447C144 447 23 310 23 161C23 47 89 -12 179 -12C312 -12 429 106 429 244C429 303 419 344 368 386L371 388C404 383 440 378 474 378C507 378 530 411 548 455ZM350 274C350 191 308 25 198 25C144 25 108 75 108 157C108 264 170 395 276 395C296 395 320 384 333 360C347 334 350 316 350 274Z" id="g113-240"></path></g><g transform="matrix(.013,0,0,-0.013,7.347,0)"><path d="M300 -147C201 -63 143 98 143 270S200 602 300 686L282 710C136 610 70 450 70 271V270C70 89 136 -72 282 -170L300 -147Z" id="g113-41"></path></g><g transform="matrix(.013,0,0,-0.013,11.845,0)"><path d="M324 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Discrete Dynamics in Nature and Society

fig6

Figure 6

Figure 6: Reconstruction of the Time-Dependent Volatility Function Using the Black–Scholes Model 