You.ve de.cid.ed t.o at.te.m.pt to val.u.e a cal.l op.tio.n o.n Br.e.nt cr.ude w.hich expires in exactly one month. The st/rike /pric/e of the/ optio/n i/s $120 whil/e the c/urren/t pri/ce o/f is $112. Yo/u es/tim/ate tha/t th/re/ is a 60% cha/nc/e th/e pric/e of /Bre/nt c/ru/de ris/es t/o $130 and th/e rest of /the /tim/e the/ pric/e is expe/cte/d to ret/reat to $105. You/ a/lso kn/ow that th/e US/ T-b/ill is yielding 0.25% EAR ov//er the/ fou/r-we/ek ho/izon.

Wh/at i/s the price of this o.ptio.n u.sing t.he.bin.om.ial .od.el? Be certai.n to s.tate th.e del.ta (number of shares) n.eede.d to hed.ge on.e lon.g call op.tion. Comment on the realism of this model, both in .de.sign and in application.

You.ve dec.ided to impr.ove your estimate of the call option using the Black-.Scholes model. Yo. have. estimated th.e an.nual stan.dard d.eviation of t.he price of Bre.nt to be 44%. What is your re.vised price estim.ate on this option? Provide an argum.ent w.hy the B.lack Sch.oles is a more re.alistic model than a one stage bin.omial m.odel. Next, p.rovide a.n argument why the Bl.ack. Scholes i.s less real.istic .than .a .multi-st.age .binomial model.

Roger, your colleague, observes that the price of the put option on Brent crude with the same expiration date and strike price is trading for $11. Is there an arbitrage? What might explain this discrepancy other than an arbitrage opportunity?