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REPRODUCE THE DERIVATIONS OF BLACK- SCHOLES FORMULA TO OBTAN THE FORMULA FOR THE ARBITRAGE FREE PUT OPTION PRICE. USE THIS FORMULA TO FIND THE PUT

REPRODUCE THE DERIVATIONS OF BLACK- SCHOLES FORMULA TO OBTAN THE FORMULA FOR THE ARBITRAGE FREE PUT OPTION PRICE. USE THIS FORMULA TO FIND THE PUT OPTION PRCE WTH THE EXERCSE PRCE OF 0.2 DOLLARS AND WTH THE MATURITY DURATION OF 6 MONTHS AFTER THE END DATE OF THE FOLLOWNG DATA SET, AND THE NOMINAL INTEREST RATE IS 10%.

(PLEASE CHECK ALL THE ASSUMPTIONS NEEDED TO APPLY THE FORMULA, IF SOME OF THE ASSUMPTIONS DO NOT HOLD, PLEASE JUST GNORE THEM AND CONTINUE WITH APPLYING THE FORMULA. THE MAIN POINT IS, I WANT TO SEE HOW YOU APPLY THE ASSUMPTIONS CHECK)

THE FOLLOWNG ARE THE CRUDE OIL PRICES

Date ln(X_t) where X_t= Crude Oil Price

1.12.1995

-2,089761011

1.01.1996

-2,103384597

1.02.1996

-2,095308697

1.03.1996

-1,985125718

1.04.1996

-1,890522111

1.05.1996

-1,996059933

1.06.1996

-2,036350267

1.07.1996

-1,996600206

1.08.1996

-1,968296263

1.09.1996

-1,883057417

1.10.1996

-1,848992252

1.11.1996

-1,901118727

1.12.1996

-1,83517754

1.01.1997

-1,845763957

1.02.1997

-1,972754417

1.03.1997

-2,029876899

1.04.1997

-2,092915271

1.05.1997

-2,038154365

1.06.1997

-2,123076478

1.07.1997

-2,100611687

1.08.1997

-2,087935223

1.09.1997

-2,09746907

1.10.1997

-2,02767777

1.11.1997

-2,081546415

1.12.1997

-2,178367645

1.01.1998

-2,271588993

1.02.1998

-2,311264627

1.03.1998

-2,378213689

1.04.1998

-2,351868597

1.05.1998

-2,392620158

1.06.1998

-2,478050599

1.07.1998

-2,450221092

1.08.1998

-2,503936014

1.09.1998

-2,392101691

1.10.1998

-2,432722965

1.11.1998

-2,547132187

1.12.1998

-2,679271237

1.01.1999

-2,580799877

1.02.1999

-2,618386001

1.03.1999

-2,419609921

1.04.1999

-2,258369226

1.05.1999

-2,235602272

1.06.1999

-2,227745891

1.07.1999

-2,116969627

1.08.1999

-2,061765063

1.09.1999

-1,949731506

1.10.1999

-2,004840787

1.11.1999

-1,908666998

1.12.1999

-1,867545845

1.01.2000

-1,82919088

1.02.2000

-1,756505891

1.03.2000

-1,74413958

1.04.2000

-1,893032388

1.05.2000

-1,783151762

1.06.2000

-1,688247351

1.07.2000

-1,75805481

1.08.2000

-1,71049707

1.09.2000

-1,633928932

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