Daidaitaccen Farashin ASIC na Cryptocurrency: Hanyar Ka'idar Zabi (Options)

1. Gabatarwa

Cryptocurrencies na Proof-of-Work (PoW) kamar Bitcoin sun dogara da na'urori na musamman (ASICs) don ayyukan ma'adinai waɗanda ke kiyaye cibiyar sadarwa, tare da ma'adinai suna karɓar sabbin alamun kuɗi a matsayin lada. Ganin ribar da ake samu daga ma'adinai ya haifar da buƙatu mai ƙarfi ga wannan kayan aikin, duk da manyan farashin aiki kamar wutar lantarki. Wannan takarda tana ƙalubalantar ilimin gargajiya kan yadda ake kimanta wannan kayan aikin, tana ba da shawarar cewa ma'adinai a zahiri tarin zaɓi ne na kuɗi (bundle of financial options) maimakon kayan aiki mai sauƙin samar da kuɗaɗe.

2. Muhimman Ra'ayoyi & Bayanin Matsala

Takardar ta gano babban rarrabuwar kawuna a cikin tattalin arzikin ma'adinai: ana karɓar lada a cikin cryptocurrency mai sauyi (misali, BTC), yayin da ake biyan kuɗin aiki (wutar lantarki, kayan aiki) a cikin kuɗin ƙasa (misali, USD). Wannan yana haifar da matsayi mai sarƙaƙƙiya na kuɗi wanda lissafin ribar zuba jari mai sauƙi ba ya kama shi.

2.1 Ma'adinai a matsayin Tarin Zabi (Option Bundle)

Babban fahimta shine cewa na'urar ma'adinai tana wakiltar tarin zaɓi na gaske (bundle of real options). A duk lokacin da ma'adinan ya yanke shawarar kunna na'urar, a zahiri suna aiwatar da zaɓi don canza wutar lantarki (farashi a USD) zuwa alamun cryptocurrency. Ma'adinan zai "aiwatar" wannan zaɓin ne kawai lokacin da ƙimar alamun da ake tsammanin za a haƙa ta wuce farashin wutar lantarki. Wannan zaɓin yana da ƙima ta asali.

2.2 Aibobi a cikin Tsarin Farashin Hashprice na Sauti (Naïve)

Shahararrun lissafin ma'adinai sun dogara da ma'auni mai suna hashprice (Ma'anar 1), wanda ke lissafin ribar da ake tsammani a kowane raka'a na lissafi (misali, kowace terahash). Babban aibi shine cewa waɗannan tsarin yawanci suna ɗauka cewa farashin cryptocurrency na gaba ya tsaya tsayin daka ko kuma ana tsammaninsa, suna yin watsi da gaba ɗaya haɗari da sauyi (volatility) da ke tattare da lada. Suna ɗaukar ma'adinai a matsayin annuiti mai sauƙi, ba a matsayin kayan aiki mai haɗari, mai cike da zaɓi ba.

3. Tsarin Farashi na Tushen Zabi (Options-Based)

Marubutan sun ƙirƙiri tsarin farashi na yau da kullun bisa ka'idar zaɓi don daidaita kimanta ma'adinan ASIC.

3.1 Tsarin Lissafi (Mathematical Formulation)

Ana iya tsara ƙimar na'urar ma'adinai a matsayin jimlar jerin zaɓi na Turai (European call options). Ga na'ura mai ƙimar hashrate $H$, amfani da wutar lantarki $P$, da farashin wutar lantarki $C$ a kowace kWh, ribar don lokaci guda (misali, rana ɗaya) idan ana haƙa ma'adinai ita ce:

$\pi(t) = H \cdot R(t) \cdot S(t) - P \cdot 24 \cdot C$

Inda $R(t)$ shine lada na ma'adinai a kowane raka'a hash a lokacin $t$, kuma $S(t)$ shine farashin lokaci na cryptocurrency. Ma'adinan zai yi aiki ne kawai idan $\pi(t) > 0$. Wannan lada daidai yake da na zaɓi na kira (call option) akan alamun da aka haƙa tare da farashin yin amfani da shi (strike price) daidai da farashin wutar lantarki. Saboda haka, jimlar ƙimar na'urar $V$ a tsawon rayuwarta $T$ ita ce:

$V = \sum_{t=1}^{T} e^{-rt} \cdot \mathbb{E}^{Q}[\max(H \cdot R(t) \cdot S(t) - P \cdot 24 \cdot C, 0)]$

inda $\mathbb{E}^{Q}$ shine tsammanin a ƙarƙashin ma'aunin rashin haɗari (risk-neutral measure), kuma $r$ shine ƙimar rashin haɗari (risk-free rate). Wannan yana canza kimantawa daga tsarin lissafin kuɗaɗe mai ragi mai sauƙi zuwa matsalar farashin zaɓi.

3.2 Sauyin Farashi (Volatility) a matsayin Mai Tafiyar da Kimar Daraja

Sakamako mai ban mamaki amma mai mahimmanci na tsarin shine cewa ƙarin sauyin farashin cryptocurrency yana ƙara ƙimar kayan aikin ma'adinai. A cikin farashin zaɓi (misali, a cikin tsarin Black-Scholes), ƙimar zaɓi tana ƙaruwa tare da sauyin kayan aikin da ke ƙasa ($\sigma$). Tunda na'urar ma'adinai tarin zaɓi ne, ƙimarta tana da alaƙa ta gaba da sauyin farashin cryptocurrency na gaba. Wannan ya saba wa ra'ayin sauti (naïve) cewa sauyi (volatility) haɗari ne kawai wanda ke rage ƙimar kayan aiki.

4. Bincike na Kwarewa & Sakamako

Takardar ta tabbatar da tsarinta ta hanyar kwatantawa ta hanyar kwarewa da dabarun maimaitawa.

4.1 Kwatantawa da Mashahuran Lissafin Ma'adinai (Mining Calculators)

Marubutan sun kwatanta farashin da tsarin su na tushen zaɓi ya ba da shawara da na manyan lissafin ribar ma'adinai. Binciken ya nuna cewa lissafin gargajiya a tsarin su suna rashin kimanta kayan aikin ma'adinai saboda sun kasa faranta zaɓin da aka saka da ƙimar sauyi. Suna lissafin kawai kudaden da ake tsammani, suna yin watsi da ƙimar "inshora" na iya rufewa a lokutan da ba su dace ba.

4.2 Maimaita Ayyukan Portfolio (Replicating Portfolio Performance)

Don tabbatar da kuskuren farashi, marubutan sun gina portfolio mai maimaitawa (replicating portfolio) ta amfani da kayan aikin kuɗi waɗanda ke kwaikwayon lada na na'urar ma'adinai. Wannan portfolio na iya ƙunshi bond marar haɗari da matsayi a cikin cryptocurrency kanta (ko abubuwan da aka samo daga gare ta), ana daidaita su a hankali don nuna zaɓin. Bincikensu na tarihi ya nuna cewa kudaden da aka samu daga wannan portfolio na kuɗi marar aiki sun fi kudaden da aka samu daga ma'adinai na gaske. Wannan alama ce ta gargajiya na arbitrage: da an daidaita farashin kayan aikin daidai, ya kamata kudaden su zama daidai, tare da la'akari da haɗari. Gaskiyar cewa ba haka ba ne tana nuna ma'adinai suna biyan kuɗi fiye da kima ga ASICs.

5. Tasiri ga Tsaron Cibiyar Sadarwa (Network Security)

Tsarin yana da tasiri mai zurfi ga tsaron blockchain:

Haɗin Sauyi-Tsaro (Volatility-Security Link): Idan sauyin farashin tsabar kuɗi ya ragu (misali, yayin da ta girma), ƙimar kayan aikin ma'adinai na tushen zaɓi ta faɗi. Wannan na iya haifar da ficewar ma'adinai na hankali, yana rage hashrate na cibiyar sadarwa kuma yana iya yin illa ga tsaronta daga hare-haren 51%, damuwa da aka maimaita a cikin bincike kamar "A kan Rashin Kwanciyar Hankali na Bitcoin Ba tare da Ladan Block ba" (Carlsten et al., 2016).
Halin Ma'adinai: Tsarin ya ba da hujja a hukumance ga halayen ma'adinai da aka lura kamar ƙaura na yanayi da rufewa na dabarun—suna aiwatar da zaɓinsu cikin hankali.
Rage Tallafin (Subsidy Phase-Out): Yayin da ladan block ke raguwa a tsawon lokaci (misali, rabin Bitcoin), kuɗin ma'amala zai zama mafi mahimmanci. Ana iya faɗaɗa tsarin zaɓi don kimanta kayan aiki bisa kuɗin shiga na kuɗi, wanda wataƙila ya fi sauyi.

6. Bincike Mai Zurfi & Hangen Nesa na Kwararru

Babban Fahimta: Kasuwar ASIC na Bitcoin ta karye a zahiri, tana kimanta kayan aiki kamar tarakta mai iya tsinkaya alhali kuwa a zahiri tarin abubuwan da aka samo daga kuɗi ne na musamman (exotic financial derivatives). Ma'adinai, sau da yawa masana fasaha, suna biyan kuɗi mai yawa don sarƙaƙiyar aiki yayin da suke yin watsi da kwafin kuɗi mai sauƙi, mai tsafta na ladansu da ake samu a kowane babban kasuwa.

Tsarin Hankali (Logical Flow): Yaish da Zohar sun sake tsara shawarar ma'adinan cikin hazaka daga "Shin zan sami riba a matsakaita?" zuwa "Shin ina da haƙƙin, amma ba wajibi ba, don samun riba?" Wannan canji daga ƙimar da ake tsammani zuwa da'awar da ta dogara da sharadi shine dukan wasan. Yana bayyana dalilin da yasa ma'adinai ke ci gaba a lokacin faɗuwar farashi—zaɓin yin ma'adinai yana riƙe da ƙima ko da aiwatar da shi nan take ba ya. Portfolio ɗin su mai maimaitawa shine harbin kashewa: idan za ka iya ƙirƙirar kudaden ma'adinai ta hanyar haɗa bond da farashin lokaci na BTC, kuma ya yi mafi kyau, to kayan aiki na zahiri suna da "amfanin dacewa" mara kyau (negative convenience yield). Kana biyan ƙarin kuɗi don wahala.

Ƙarfi & Aibobi: Ƙarfin shine kyawun salo da goyon bayan kwarewa na hujjar arbitrage. "Shaida ta hanyar maimaitawa" ce mai gamsarwa. Aibin, gama gari a cikin tsarin kuɗi, shine dogaro da wasu mahimman zato: kasuwa mai ruɗi da inganci don cryptocurrency na asali, ikon daidaita portfolio mai maimaitawa akai-akai (wanda ke da farashin ma'amala), da kwanciyar hankali na sigogin cibiyar sadarwa kamar hashrate da wahala. Ƙaruwar hashrate kwatsam, wanda ba a zata ba, tana canza lada $R(t)$ ga kowa, haɗarin da ke da alaƙa wanda portfolio na BTC da bond kawai ba su kama shi sosai ba. Wannan yana kama da haɗarin tsarin da aka haskaka a cikin babban aikin kan Long-Term Capital Management.

Fahimta Mai Aiki (Actionable Insights): 1) Ga Ma'adinai: Kafin sayi wannan S21 na gaba, gudanar da tsarin zaɓi. Farashin da ya dace yana iya zama ƙasa da farashin da masana'anta ya faɗa. Yi la'akari da ware jari ga portfolio mai maimaitawa maimakon. 2) Ga Masu Zuba Jari: Harkar ma'adinai na iya zama da kuskuren farashi a tsarin. Nemi kamfanoni waɗanda kimantawar su ta dogara da tsarin farashin hashprice na sauti—za su iya zama tarko na ƙima. 3) Ga Masu Ƙirƙirar Ƙa'idar (Protocol Designers): Gane cewa tsaron PoW ba aiki ne kawai na farashi ba, amma na sauyin farashi (volatility). Ƙirƙirar don ƙarin kasuwanni masu kwanciyar hankali na kuɗi ko haɗa sigogi masu dogaro da sauyi, kamar yadda wasu binciken Ethereum ya ba da shawarar, na iya zama mahimmanci ga tsaro na dogon lokaci.

7. Tsarin Fasaha & Misalin Lamari

Misalin Tsarin Bincike (Ba Code ba):

Yi la'akari da kimanta Antminer S19 XP (140 TH/s, 3010W) don tsawon rayuwar shekaru 2. Lissafi na yau da kullun zai iya:

Ɗauka cewa farashin Bitcoin na gaba ya tsaya tsayin daka (misali, $60,000).
Ƙididdige kuɗin shiga na yau da kullun na BTC bisa wahalar cibiyar sadarwa ta yanzu.
Cire farashin wutar lantarki na yau da kullun a $0.05/kWh.
Rage jerin ribar shekaru 2 a babban ƙimar ragi na "haɗari" na sabani (misali, 15%).
Iso ga "daidaitaccen" farashin kayan aiki na $4,000.

Tsarin Tushen Zabi (Options-Based Framework) zai:

Ƙirƙirar Tsarin Asali (Model the Underlying): Yi amfani da tsarin sauyi (stochastic model) (misali, Geometric Brownian Motion) don farashin Bitcoin na gaba, an daidaita shi da sauyinsa da aka nuna (implied volatility) daga kasuwannin abubuwan da aka samo daga gare ta (derivatives markets) (misali, 70% na shekara).
Ayyana Jerin Zabi (Define the Option Series): ɗauki kowace rana a matsayin zaɓi na Turai (European call option) daban. "Farashin yin amfani da shi" (Strike price) na Rana t shine farashin USD na wutar lantarki na wannan rana: $Strike_t = 3.01 kW * 24h * $0.05/kWh = $3.61$.
Ƙayyade Kayan Lada (Determine the Payoff Asset): Adadin kayan aikin da ke ƙasa don kowane zaɓi shine adadin BTC da ake tsammanin za a haƙa a wannan rana, wanda kansa ya dogara da haɓakar hashrate na cibiyar sadarwa. Wannan yana ƙara wani yanayi na sarƙaƙiya, yana ƙirƙirar daidaitawar wahala.
Faranta Tarin (Price the Bundle): Yi amfani da hanyoyin lambobi (numerical methods) (kamar simintin Monte Carlo) don kimanta jimillar waɗannan zaɓi na kowace rana 730 a ƙarƙashin ma'aunin rashin haɗari (risk-neutral measure). Wannan farashin zai zama mafi girma fiye da na tsarin sauti na $4,000 saboda ya haɗa da ƙimar sauyi mai kyau. Tsarin na iya fitar da ƙimar da ta dace na $5,500.
Binciken Arbitrage (Arbitrage Check): Gina portfolio mai maimaitawa. Don sauƙi, ce tarin zaɓin "delta" (sensitivity to BTC price) daidai yake da riƙe 0.1 BTC. Dabarar maimaitawa ta ƙunshi riƙe $5,500 a cikin haɗin 0.1 BTC da bond marar haɗari, ana sake daidaita su kowace rana bisa ga canjin delta na zaɓin. Simintin tarihi zai gwada ko kudaden shiga na wannan portfolio sun wuce kawai sayan S19 XP da yin ma'adinai.

8. Aikace-aikace na Gaba & Hanyoyin Bincike

Kayayyakin Kuɗi na Rarrabuwa (Decentralized Finance - DeFi): Ra'ayin portfolio mai maimaitawa ana iya samar da shi azaman samfur. Za mu iya ganin fitowar alamun "ma'adinai na roba" (synthetic mining) ko rumbuna waɗanda ke amfani da zaɓi da riƙon farashin lokaci don samar da jerin amfanin ƙasa da ke kwaikwayon fitar da wani ASIC na musamman, yana ba da damar shiga tattalin arzikin ma'adinai ba tare da kayan aiki ba.
Gudanar da Haɗari na Ci Gaba don Gonakin Ma'adinai (Mining Farms): Manyan ayyuka na iya amfani da wannan tsarin don kare matsayinsu daidai. Maimakon kawai sayar da samar da BTC na gaba, za su iya tsara abubuwan da ke kewaye da tsarin wuya, matsayi, da sauran dabarun zaɓi a kusa da fitar da hash da ake tsammani, suna inganta don zaɓin da suke da shi.
Kimanta Masu Tabbatar da Proof-of-Stake (PoS): Duk da yake PoS ba shi da zaɓin canza wutar lantarki, yana da wasu nau'ikan zaɓi (misali, zaɓin sake saka jari, zaɓin canza ayyukan tabbatarwa, ƙimar zaɓi na haɗarin yanke). Yin amfani da ka'idar zaɓi na gaske don kimanta ƙimar kumburin PoS mataki ne na gaba na hankali.
Binciken Haɗin Kai & Saye (Merger & Acquisition - M&A): Wannan tsarin yana ba da kayan aiki mafi ƙarfi don kimanta kamfanonin ma'adinai yayin saye, yana motsawa bayan ma'auni mai sauƙi na farashi-zuwa-riba (price-to-earnings) bisa farashin hashprice na yanzu.
Ƙirƙirar Ƙirar Ƙa'idar (Protocol Design Innovation): Shin za a iya ƙirƙirar sabbin hanyoyin yarjejeniya inda kasafin tsaro a fili ya lissafa kuma ya yi amfani da wannan ƙimar zaɓi? Bincike zai iya bincika hanyoyin ba da lada masu daidaitawa da sauyi (volatility-adjusted).

9. Nassoshi

Yaish, A., & Zohar, A. (2023). Daidaitaccen Farashin ASIC na Cryptocurrency: Shin Ma'adinai Suna Biyan Kuɗi Fiye da Kima? A cikin Proceedings of the 5th Conference on Advances in Financial Technologies (AFT 2023). https://doi.org/10.4230/LIPIcs.AFT.2023.2
Cikakken Sigar: Yaish, A., & Zohar, A. (2020). Daidaitaccen Farashin ASIC na Cryptocurrency: Shin Ma'adinai Suna Biyan Kuɗi Fiye da Kima? arXiv preprint arXiv:2002.11064. https://arxiv.org/abs/2002.11064
Nakamoto, S. (2008). Bitcoin: Tsarin Kuɗi na Peer-to-Peer na Lantarki.
Carlsten, M., Kalodner, H., Weinberg, S. M., & Narayanan, A. (2016). A kan Rashin Kwanciyar Hankali na Bitcoin Ba tare da Ladan Block ba. A cikin Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security.
Hull, J. C. (2018). Zaɓi, Nan gaba, da Sauran Abubuwan da aka samo daga gare su (10th ed.). Pearson. (Don ka'idar zaɓi ta asali).
Easley, D., O'Hara, M., & Basu, S. (2019). Daga Ma'adinai zuwa Kasuwanni: Juyin Halitta na Kuɗin Ma'amala na Bitcoin. Journal of Financial Economics.